Mas
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Mas as PDF for free.
More details
- Words: 4,607
- Pages: 19
QUANTITATIVE TECHNIQUES (MANAGEMENT CONSULTANCY) PROBLEM 1 (PERT/CPM) The management of SHOPEE COMPANY has approved the nationwide promotion of its new product βESPRITβ and the following activity list has been prepared together with prerequisite activities for immediate predecessor(s) and time estimates. Activities Symbol Description A Develop advertising plan B Develop the plan for promotion and advertising material C Design training programs for branch managers D Schedule advertisements (radio, TV and dailies) E Develop advertising materials F Prepare promotion material for use in inbranch promo G Prepare training materials for branch managers H Conduct pre-introduction campaign to the media I Screen and select branch managers to be trained J Conduct Training program K In-branch introduction of the product βESPRITβ
Prerequisite Activities -
Time Estimates in Weeks π‘π π‘π 2 3 2 3
π‘π 1 1
-
1
2
3
A
1
3
5
A B
1 4
4 7
13 10
B
3
6
9
D,E
5
7
9
C
2
4
6
G, I F,H,J
2 1
3 1
4 1
Required: 1. Construct the Pert network of the above activities. 2. Identify the critical path and determine the earliest completion time for the project. 3. Compute the slack time for each activity. Suggested Solution: Activities Symbol Description A Develop advertising plan B Develop the plan for promotion and advertising material C Design training programs for branch managers D Schedule advertisements (radio, TV and dailies) E Develop advertising materials F Prepare promotion material for use in in-branch promo
Prerequisite Activities -
Time Estimates in Weeks π‘π π‘π 2 3 2 3
π‘π 1 1
-
1
2
3
2
A
1
3
5
3
A B
1 4
4 7
13 10
5 7
π‘π 2 2
G H I J K
Prepare training materials for branch managers Conduct pre-introduction campaign to the media Screen and select branch managers to be trained Conduct Training program In-branch introduction of the product βESPRITβ
B
3
6
9
6
D,E
5
7
9
7
C
2
4
6
4
G, I F,H,J
2 1
3 1
4 1
3 1
1. Construct the Pert network of the above activities. 5
2 D
3
4
7
7
2
0 A
2
0
2 2
7 E
9 F
B
2
7
5
2
14
7
7
2 START
7
5
2
0
14 H
14
7
1
14
14
FINISH 15
2
3
8 G
6
5
11
9
12
J
3
11 0 C
15 K
2
2
4
4
I
2
2
14
9 7
11
2. Identify the critical path and determine the earliest completion time for the project. a. Completion Time: 15 Weeks b. Critical Path: A-E-H-K 5
2 D
3
4
7
7
2
0 A
2
0
2 2
7 E
9 F
B
2
7
5
2
14
7
7
2 START
14
7 14
14
8 G
6
5
11
9
12
J 11 0 C
2
2
4
4
9 I
2
15 K
2
3
2
7
5
2
0
14 H
7
11
3 14
1
FINISH 15
3. Compute the slack time for each activity. 5
2 D
0
2
3
4
7
7
2
0 A
0
2
0
2 2
7 E
0
2 B
3
7
2
9
14
7
5
0 14
7 14
2
8
14
G
2
11
9
12
J 2
2 C
FINISH 15
6
5
2
1
3 5
0
15 K
7
2
3
0
7
5
2
F
START
14 H
2
2
4
4
9 I
2
11
3 14
7
11
PROBLEM 2 (PERT/CPM) The following table contains information related to the major activities of a research project. Activity A B C D E F
Post β Activity C,B I D I F J
Expected Time (Days) 5 7 8 2 3 6
Required: 1. Draw the PERT/CPM network 2. Find the critical path 3. Determine the expected length of the project
Activity G H I J K
Post β Activity H K J END END
Expected Time (Days) 1 2 10 8 17
Suggested Solution: 1. Draw the PERT/CPM network 5
12 B
I
8 0
15
15
13
13
10 25
5
A
5 5
0
5 C
13
E
F
0
1
14
33
FINISH
25
3 H
1
13
25
6
19
1 G
8
9
3
19
33 J
15
3
16
25
2
13
3
0
15 D
8
5
START
25
15
7
3
20
2
K
14
17 33
16
16
2. Find the critical path Critical Path: A-C-D-I-J 5
12 B
8 0
A
15
15
13
13
10 25
5 5 5 C 5
E
13
0
1
19
1
14
3. Determine the expected length of the project Expected Length of the Project: 33 days
14
25
33
FINISH
6 25
3 H
8
9
F
1
33 J
15
3
19
25
2
13
3
16
G
15 D
8
3
0
13
I
5
0
START
25
15
7
3
2
20 K
16
16
17 33
PROBLEM 3 (PERT/CPM) Following are a set of activities for a project, their predecessor restrictions and the three time estimates of completion time. Activity A B C D E F G H I
Predecessors None None None A B B C D,E F,G,H
Optimistic 1 1 3 3 3 5 5 2 5
Most Likely 3 2 5 4 4 6 6 8 6
Pessimistic 5 3 7 5 5 13 13 14 13
Required: 1. Construct the PERT network of the above activities. 2. Identify the critical path and determine the earliest completion time for the project. 3. Compute the slack time for each activity. Suggested Solution: 1. Construct the PERT network of the above activities. Activity A B C D E F G H I
Predecessors None None None A B B C D,E F,G,H 3
0
A
Optimistic 1 1 3 3 3 5 5 2 5 3
0
3
3
7
2
6 E
B
2
3
3
2
7
15
7
8 15
4 7
2
1 START
9 F
0
5
12
G 8
22 I
15
5
5
15
7
8
C
Expected 3 2 5 4 4 7 7 8 7
4
H
0
Pessimistic 5 3 7 5 5 13 13 14 13
7
D
3
Most Likely 3 2 5 4 4 6 6 8 6
7 15
15
END
7 22
2. Identify the critical path and determine the earliest completion time for the project. Critical Path: A-D-H-I 3
0
A
3
0
7
D
3 3
4
3
7
7
15 H
2
B
2
3
3
2
15
4 7
2
1 START
9 F
0
5
22 I
15
5
5
15
7
8
C
7
6 E
0
8
END
7 22
15
12
G
7
8
15
Estimated Project Completion Time: 22 Days 3. Compute the slack time for each activity. 3
0
A
0
3 D
3
0
7
3
0
4
3
0
7
7
15 H
2 2
0 B
6 E
1
3
7
2
9
START
F
C 3
8 15
6
0 15
7
22 I
8
15
5
5
12
8
8
3 0
7
4
3
2
1
1
15
END
7 22
3
5
G
7 15
PROBLEM 4 (DECISION UNDER UNCERTAINTY) Abigail Posadas is the principal owner of Brown Oil, Inc. After quitting her university teaching job, Abi has been able to increase her annual salary by a factor of over 100. At the present time, Abi is forced to consider purchasing some more equipment for Brown Oil because of competition. Her alternatives are shown in the following table: Equipment Sub 100 Oiler J Texan
Favorable Market Php 300,000 Php 250,000 Php 75,000
Required: Under the following approaches, what would be Abiβs decision? 1. Optimistic Approach 2. Pessimistic Approach
Unfavorable Market (Php 200,000) (Php 100,000) (Php 18,000)
3. Criterion of Realism (πΌ = 0.65) 4. Equally Likely 5. Minimax Regret Suggested Solutions 1. Optimistic Approach Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
300,000.00
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
250,000.00
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
75,000.00
Choose Sub 100 as it has estimated monetary value of Php 300,000 2. Pessimistic Approach Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
(200,000.00)
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
(100,000.00)
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
(18,000.00)
Do nothing as the available options will results to net loss 3. Criterion of Realism (πΌ = 0.65) Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
125,000.00
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
127,500.00
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
42,450.00
Choose Oiler J because it has highest estimated monetary value of Php 127,500 4. Equally Likely Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
50,000.00
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
75,000.00
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
28,500.00
5. Minimax Regret Payoff Table Equipment
Favorable Market
Unfavorable Market
Sub 100
PHP
300,000.00
PHP
(200,000.00)
Oiler J
PHP
250,000.00
PHP
(100,000.00)
Texan
PHP
75,000.00
PHP
(18,000.00)
Highest Payoff
PHP
300,000.00
PHP
(18,000.00)
Opportunity Loss Table Equipment
Favorable Market
Sub 100
PHP
Oiler J
PHP
Texan
PHP
-
Unfavorable Market
Max OL
PHP
182,000.00
PHP
182,000.00
50,000.00
PHP
82,000.00
PHP
82,000.00
225,000.00
PHP
-
PHP
225,000.00
Choose Oiler J because it has the lowest Opportunity Loss of Php 82,000 based on the table.
PROBLEM 5 (DECISION UNDER UNCERTAINTY) Todayβs Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for advising the president of Todayβs Electronics on electronic manufacturing equipment, has developed the following table concerning a proposed facility: Facility Large Medium Small No Facility
Strong Market Php 550,000 Php 300,000 Php 200,000 Php 0
Fair Market Php 110,000 Php 129,000 Php 100,000 Php 0
Required: Under the following approaches, what would be the managerβs decision? 1. 2. 3. 4. 5.
Optimistic Approach Pessimistic Approach Criterion of Realism (πΌ = 0.58) Equally Likely Minimax Regret
Poor Market (Php 310,000) (Php 100,000) (Php 32,000) Php 0
Suggested Solutions: 1. Optimistic Approach Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP
550,000.00
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP
300,000.00
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
200,000.00
No Facility
PHP
PHP
PHP
-
-
Payoff
(32,000.00) -
PHP
-
Choose to build Large Facility. 2. Pessimistic Approach Facility
Strong Market
Fair Market
Poor Market
Payoff
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP (310,000.00)
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP (100,000.00)
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
No Facility
PHP
PHP
PHP
-
-
(32,000.00) -
(32,000.00)
PHP
-
Donβt build facility. 3. Criterion of Realism (πΌ = 0.58) Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP
188,800.00
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP
132,000.00
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
102,560.00
No Facility
PHP
PHP
PHP
-
-
Payoff
(32,000.00) -
PHP
-
Choose to build Large Facility. 4. Equally Likely Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP
116,666.67
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP
109,666.67
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
89,333.33
No Facility
PHP
PHP
PHP
Choose to build Large Facility.
-
-
Payoff
(32,000.00) -
PHP
-
5. Minimax Regret Payoff Table Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
Small
PHP 200,000.00
PHP 100,000.00
PHP
No Facility
PHP
PHP
-
PHP
-
Highest Payoff
PHP 550,000.00
PHP 129,000.00
PHP
-
-
(32,000.00)
Opportunity Loss Table Facility
Strong Market
Fair Market
Poor Market
Max OL
Large
PHP
-
PHP
19,000.00
PHP
310,000.00
PHP
310,000.00
Medium
PHP 250,000.00
PHP
-
PHP
100,000.00
PHP
250,000.00
Small
PHP 350,000.00
PHP
29,000.00
PHP
32,000.00
PHP
350,000.00
No Facility
PHP 550,000.00
PHP 129,000.00
PHP
PHP
550,000.00
-
Choose to build Medium Facility PROBLEM 6 (DECISION UNDER RISK) A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (i.e., there is a favorable market for the clinic), the physicians could realize a net profit of Php 10,000,000. If the market is not favorable, they could lose Php 400,000. Of course, they donβt have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50β50 chance the clinic will be successful. Required: Construct a decision tree to help analyze this problem. What should the medical professionals do? Suggested Solutions:
Php 0
Do Nothing EMV = Php 0
Php 10,000,000 Favorable Market (50%) EMV = Php 10,000,000 x 50% = Php 5,000,000 Construct a Clinic EMV = Php 4,200,000
Unfavorable Market (50%) Php (400,000) EMV = Php (400,000) x 50% = Php (200,000) Build a clinic as it will give the medical profession an estimated monetary value of Php 4,200,000. PROBLEM 7 (DECISION UNDER RISK) The physicians in Problem 6 have been approached by a market research firm that offers to perform a study of the market at a fee of Php 50,000. The market researchers claim their experience enables them to use Bayesβ theorem to make the following statements of probability: Probability Favorable Market Unfavorable Market
Favorable Study 82% 18%
Unfavorable Study 11% 89%
The probability that the outcome of a favorable study is 55%, while unfavorable study would results to 45% probability.
Php 9,950,000 Favorable Market (82%) EMV = Php 9,950,000 x 82% = Php 8,159,000 Build a Clinic
EMV = Php 8,078,000
Unfavorable Market (18%) EMV = Php 8,078,000
Php (450,000) EMV = Php (450,000) x 18% = Php (81,000) Do Not Build a Clinic
Php (50,000)
Favorable Survey (55%) EMV = Php 8,078,000 x 55% = Php 4,447,850
EMV = Php 9,950,000 x 11% = Php 1,094,500 Php 9,950,000
Favorable Market (11%)
EMV = Php 694,000 x 45% = Php 312,300 EMV = Php 694,000 Unfavorable Survey (45%) Build a Clinic Conduct Market Survey Unfavorable Market (89%) EMV = Php 4,760,150 EMV = Php 694,000
Php (450,000) EMV = Php (450,000) x 89% = Php (400,500)
Do Not Build a Clinic Php (50,000) EMV = Php 10,000,000 x 50% = Php 5,000,000 Php 10,000,000 Favorable Market (50%) Do Not Conduct Market Survey
EMV = Php 4,200,000
EMV = Php 4,200,000 Build a Clinic Unfavorable Market (50%) EMV = Php 4,200,000
Php (400,000) EMV = Php (400,000) x 50% = Php (200,000)
Do Not Build a Clinic Php 0
The decision should be to conduct a survey and in either results of the survey, build a clinic.
PROBLEM 8 (REGRESSION ANALYSIS) Vianne Jane Ibarreta runs a florist shop on the Quezon City, specializing in floral arrangements for weddings and other special events. She advertises weekly in the local newspapers and is considering increasing her advertising budget. Before doing so, she decides to evaluate the past effectiveness of these ads. Five weeks are sampled, and the advertising peso and sales volume for each of these is shown in the following table. Advertising Php 5,000 Php 3,000 Php 7,000 Php 2,000 Php 8,000
Sales Php 11,000 Php 6,000 Php 10,000 Php 6,000 Php 12,000
Required: a. b. c. d. e.
Determine the mean of the dependent variable. Determine the mean of the independent variable. Determine the regression line. If Vianne decided to shell out Php 12,000 in advertising expense, what would be her expected sales? If Vianne wants to have sales of Php 15,000, based on the regression line, how much advertising expense should be budget?
Suggested Solutions: a. Determine the mean of the dependent variable. Dependent variable is Sales b. Determine the mean of the independent variable. Independent variable is Advertising Expenses c. Determine the regression line. πΏ 5,000 3,000 7,000 2,000 8,000 βπ = 25,000 25,000 πΜ = = 5,000 5 π1 =
π 11,000 6,000 10,000 6,000 12,000 βπ = 45,000 45,000 πΜ = = 9,000 5
Μ ) (πΏ β πΏ 0 (2,000) 2,000 (3,000) 3,000
β(π β πΜ )(π β πΜ ) 26,000,000 = = 1.00 β(π β πΜ )2 26,000,000
Μ ) (π β π 2,000 (3,000) 1,000 (3,000) 3,000
Μ )π (πΏ β πΏ 0 4,000,000 4,000,000 9,000,000 9,000,000 β = 26,000,000
Μ )(π β π Μ ) (πΏ β πΏ 0 6,000,000 2,000,000 9,000,000 9,000,000 β = 26,000,000
π0 = πΜ β π1 πΜ = 9,000 β (1.000)5,000 = 4,000
Μ = π·ππ π, πππ + πΏ π d. If Vianne decided to shell out Php 12,000 in advertising expense, what would be her expected sales? πΜ = πβπ 4,000 + π = πβπ 4,000 + 12,000 = πβπ 4,000 + πβπ 12,000 = π·ππ ππ, πππ
e. If Vianne wants to have sales of Php 15,000, based on the regression line, how much advertising expense should be budget? πΜ = πβπ 4,000 + π = πβπ 4,000 + 15,000 = πβπ 4,000 + πβπ 15,000 = π·ππ ππ, πππ PROBLEM 9 (REGRESSION ANALYSIS) Chino PateΓ±o is a real estate broker, he was able to gather the following data (selling price, square footage, number of bedrooms, and age of houses) that have sold in a neighborhood in the past 6 months. Selling Price Php 6,400,000 Php 5,900,000 Php 6,150,000 Php 7,900,000 Php 8,750,000 Php 9,250,000 Php 9,500,000 Php 11,300,000 Php 11,500,000 Php 13,800,000 Php 14,250,000 Php 14,400,000 Php 14,500,000 Php 14,750,000 Php 14,400,000 Php 15,550,000 Php 16,500,000
Square Foot 1,670 1,339 1,712 1,840 2,300 2,234 2,311 2,377 2,736 2,500 2,500 2,479 2,400 3,124 2,500 4,062 2,854
No. of Bedrooms 2 2 3 3 3 3 3 3 4 3 4 3 3 4 3 4 3
Age (In Years) 30 25 30 40 18 30 19 7 10 1 3 3 1 0 2 10 3
Required: 1. 2. 3. 4. 5.
What is the regression line if you want to determine the sales price using square foot? What is the regression line if you want to determine the sales price using no. of bedrooms? What is the regression line if you want to determine the sales price using age in years? What would be the selling price of a unit with 2,789 square foot? If a client has a budget of Php 10,000,000. What is the average years of the house should Chino suggest?
Suggested Solutions: 1. What is the regression line if you want to determine the sales price using square foot? πΏ
π
1,670 1,339 1,712 1,840 2,300 2,234 2,311 2,377 2,736 2,500 2,500
6,400,000 5,900,000 6,150,000 7,900,000 8,750,000 9,250,000 9,500,000 11,300,000 11,500,000 13,800,000 14,250,000
Μ ) (πΏ β πΏ (738.12) (1,069.12) (696.12) (568.12) (108.12) (174.12) (97.12) (31.12) 327.88 91.88 91.88
Μ ) (π β π
Μ )π (πΏ β πΏ
(5,058,823.53) (5,558,823.53) (5,308,823.53) (3,558,823.53) (2,708,823.53) (2,208,823.53) (1,958,823.53) (158,823.53) 41,176.47 2,341,176.47 2,791,176.47
544,817.66 1,143,012.54 484,579.78 322,757.66 11,689.43 30,316.96 9,431.84 968.31 107,506.84 8,442.37 8,442.37
Μ )(π β π Μ ) (πΏ β πΏ 3,734,006,920.42 5,943,036,332.18 3,695,565,743.94 2,021,830,449.83 292,871,626.30 384,595,155.71 190,236,332.18 4,942,214.53 13,501,038.06 215,112,802.77 256,459,861.59
2,479 2,400 3,124 2,500 4,062 2,854 βπ = 40,938 40,938 πΜ = 17 = 2,408.12
π1 =
14,400,000 14,500,000 14,750,000 14,400,000 15,550,000 16,500,000 βπ = 194,800,000 194,800,000 πΜ = 17 = 11,458,823.53
70.88 (8.12) 715.88 91.88 1,653.88 445.88
2,941,176.47 3,041,176.47 3,291,176.47 2,941,176.47 4,091,176.47 5,041,176.47
5,024.31 65.90 512,487.54 8,442.37 2,735,326.84 198,811.07
208,477,508.65 (24,687,197.23) 2,356,095,155.71 270,242,214.53 6,766,324,567.47 2,247,771,626.30
β = 6,132,123.76
β = 28,576,382,352.94
β(π β πΜ )(π β πΜ ) 28,576,382,352.94 = = 4,660.11 β(π β πΜ )2 6,132,123.76
π0 = πΜ β π1 πΜ = 11,458,823.53 β (4,660.11)2,408.12 = 236,719.45 Μ = π·ππ πππ, πππ. ππ + π, πππ. πππΏ π 2. What is the regression line if you want to determine the sales price using no. of bedrooms? πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
2 2 3 3 3 3 3 3 4 3 4 3 3 4 3 4 3 βπ = 53
6,400,000 5,900,000 6,150,000 7,900,000 8,750,000 9,250,000 9,500,000 11,300,000 11,500,000 13,800,000 14,250,000 14,400,000 14,500,000 14,750,000 14,400,000 15,550,000 16,500,000 βπ = 194,800,000
(738.12) (1,069.12) (696.12) (568.12) (108.12) (174.12) (97.12) (31.12) 327.88 91.88 91.88 70.88 (8.12) 715.88 91.88 1,653.88 445.88
(5,058,823.53) (5,558,823.53) (5,308,823.53) (3,558,823.53) (2,708,823.53) (2,208,823.53) (1,958,823.53) (158,823.53) 41,176.47 2,341,176.47 2,791,176.47 2,941,176.47 3,041,176.47 3,291,176.47 2,941,176.47 4,091,176.47 5,041,176.47
1.25 1.25 0.01 0.01 0.01 0.01 0.01 0.01 0.78 0.01 0.78 0.01 0.01 0.78 0.01 0.78
53 17 = 3.12 πΜ =
π1 =
0.01 β = 5,76
194,800,000 17 = 11,458,823.53 πΜ =
β(π β πΜ )(π β πΜ ) 20,832,352.94 = = 3,616,727.94 β(π β πΜ )2 5.76
π0 = πΜ β π1 πΜ = 11,458,823.53 β (3,616,727.94)3.12 = 174,632.36 Μ = π·ππ πππ, πππ. ππ + π, πππ, πππ. πππΏ π
Μ )(π β π Μ ) (πΏ β πΏ 5,653,979.24 6,212,802.77 624,567.47 418,685.12 318,685.12 259,861.59 230,449.83 18,685.12 36,332.18 (275,432.53) 2,462,802.77 (346,020.76) (357,785.47) 2,903,979.24 (346,020.76) 3,609,861.59 (593,079.58) β = 20,832,352.94
3. What is the regression line if you want to determine the sales price using age in years? πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
Μ )(π β π Μ ) (πΏ β πΏ
30 25 30 40 18 30 19 7 10 1 3 3 1 0 2 10 3 βπ = 232
6,400,000 5,900,000 6,150,000 7,900,000 8,750,000 9,250,000 9,500,000 11,300,000 11,500,000 13,800,000 14,250,000 14,400,000 14,500,000 14,750,000 14,400,000 15,550,000 16,500,000 βπ = 194,800,000
16.35 11.35 16.35 26.35 4.35 16.35 5.35 (6.65) (3.65) (12.65) (10.65) (10.65) (12.65) (13.65) (11.65) (3.65) (10.65)
(5,058,823.53) (5,558,823.53) (5,308,823.53) (3,558,823.53) (2,708,823.53) (2,208,823.53) (1,958,823.53) (158,823.53) 41,176.47 2,341,176.47 2,791,176.47 2,941,176.47 3,041,176.47 3,291,176.47 2,941,176.47 4,091,176.47 5,041,176.47
267.42 128.89 267.42 694.48 18.95 267.42 28.65 44.18 13.30 159.95 113.36 113.36 159.95 186.24 135.65 13.30 113.36
(82,726,643.60) (63,108,996.54) (86,814,878.89) (93,785,467.13) (11,791,349.48) (36,120,761.25) (10,485,467.13) 1,055,709.34 (150,173.01) (29,608,996.54) (29,717,820.07) (31,314,878.89) (38,461,937.72) (44,914,878.89) (34,256,055.36) (14,920,761.25) (53,673,702.42)
β = 2,725.88
β = (660,797,058.82)
232 17 = 13.65 πΜ =
π1 =
194,800,000 17 = 11,458,823.53 πΜ =
β(π β πΜ )(π β πΜ ) (660,797,058.82) = = (242,416.05) β(π β πΜ )2 2,725.88
π0 = πΜ β π1 πΜ = 11,458,823.53 β (β242,416.05)13.65 = 14,767,802.61 Μ = π·ππ ππ, πππ, πππ. ππ β πππ, πππ. πππΏ π 4. What would be the selling price of a unit with 2,789 square foot? πΜ = πβπ 236,719.45 + 4,660.11π = πβπ 236,719.45 + (4,660.11)(2,789) = π·ππ ππ, πππ, πππ. ππ 5. If a client has a budget of 10,000,000. What is the average years of the house should Chino suggest? πΜ = πβπ 14,767,802.61 β 242,416.05π β π =
π=
πβπ 14,767,802.61 β πΜ 242,416.05
14,767,802.61 β 10,000,000 4,767,802.61 = = ππ. ππ ππ¬π¨πΉπΊ 242,416.05 242,416.05
PROBLEM 10 (REGRESSION ANALYSIS) The closing stock price of Globe and PLDT was recorded over a 12-month period in 2017. The closing price for the Philippine Stocks Exchange Index (PSEi) was also recorded over this same time period. These values are shown in the following table: Month January February March April May June July August September October November December
β± β± β± β± β± β± β± β± β± β± β± β±
PSEi 7,229.66 7,212.09 7,311.72 7,661.01 7,837.12 7,843.16 8,018.05 7,958.57 8,171.43 8,365.26 8,254.03 8,558.42
β± β± β± β± β± β± β± β± β± β± β± β±
Globe (GLO) 1,720.00 1,828.00 2,032.00 2,078.00 2,110.00 2,048.00 2,116.00 2,000.00 2,050.00 2,042.00 1,830.00 1,900.00
β± β± β± β± β± β± β± β± β± β± β± β±
PLDT (TEL) 1,470.00 1,460.00 1,646.00 1,770.00 1,728.00 1,798.00 1,637.00 1,730.00 1,668.00 1,710.00 1,481.00 1,480.00
Required: 1. Based on the PSEi prices, determine the regression line of GLO stocks. 2. Based on the PSEi prices, determine the regression line of TEL stocks. 3. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in GLO stocks from December price. 4. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in TEL stocks from December price. 5. By the end of October 2018, the PSEi falls at β± 7,140.29. Determine which from the two stocks has the highest percentage decrease. Suggested Solutions 1. Based on the PSEi prices, determine the regression line of GLO stocks. πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
Μ )(π β π Μ ) (πΏ β πΏ
7,229.66 7,212.09 7,311.72 7,661.01 7,837.12 7,843.16 8,018.05 7,958.57 8,171.43 8,365.26 8,254.03 8,558.42 βπ = 94,420.52
1,720.00 1,828.00 2,032.00 2,078.00 2,110.00 2,048.00 2,116.00 2,000.00 2,050.00 2,042.00 1,830.00 1,900.00 βπ = 23,754.00
(638.72) (656.29) (556.66) (207.37) (31.26) (25.22) 149.67 90.19 303.05 496.88 385.65 690.04
(259.50) (151.50) 52.50 98.50 130.50 68.50 136.50 20.50 70.50 62.50 (149.50) (79.50)
407,958.98 430,712.19 309,866.64 43,000.93 976.98 635.88 22,402.11 8,134.84 91,841.32 246,893.05 148,728.49 476,159.80 β = 2,187,311.22
165,746.98 99,427.43 (29,224.48) (20,425.62) (4,079.00) (1,727.34) 20,430.41 1,848.96 21,365.26 31,055.21 (57,655.17) (54,858.45) β = 171,904.20
94,420.52 12 = 7,868.38 πΜ =
23,754.00 12 = 1,979.50 πΜ =
π1 =
β(π β πΜ )(π β πΜ ) 171,904.20 = = 0.0786 2 β(π β πΜ ) 2,187,311.22
π0 = πΜ β π1 πΜ = 1,979.50 β (0.0786)7,868.38 = 1,361.05 Μ = π·ππ π, πππ. ππ + π. πππππΏ π 2. Based on the PSEi prices, determine the regression line of TEL stocks. πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
Μ )(π β π Μ ) (πΏ β πΏ
7,229.66 7,212.09 7,311.72 7,661.01 7,837.12 7,843.16 8,018.05 7,958.57 8,171.43 8,365.26 8,254.03 8,558.42 βπ = 94,420.52
1,470.00 1,460.00 1,646.00 1,770.00 1,728.00 1,798.00 1,637.00 1,730.00 1,668.00 1,710.00 1,481.00 1,480.00 βπ = 19,578.00
(638.72) (656.29) (556.66) (207.37) (31.26) (25.22) 149.67 90.19 303.05 496.88 385.65 690.04
(161.50) (171.50) 14.50 138.50 96.50 166.50 5.50 98.50 36.50 78.50 (150.50) (151.50)
26,082.25 29,412.25 210.25 19,182.25 9,312.25 27,722.25 30.25 9,702.25 1,332.25 6,162.25 22,650.25 22,952.25 β = 2,187,311.22
103,152.74 112,553.16 (8,071.52) (28,720.28) (3,016.27) (4,198.58) 823.20 8,884.04 11,061.45 39,005.34 (58,040.83) (104,541.57) β = 68,890.90
94,420.52 12 = 7,868.38 πΜ =
π1 =
19,578.00 12 = 1,631.50 πΜ =
β(π β πΜ )(π β πΜ ) 68,890.90 = = 0.0315 2 β(π β πΜ ) 2,187,311.22
π0 = πΜ β π1 πΜ = 1,631.50 β (0.0315)7,868.38 = 1,383.65 Μ = π·ππ π, πππ. ππ + π. πππππΏ π
3. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in GLO stocks from December price. πΜ = πβπ 1,361.05 + 0.0786π = πβπ 1,361.05 + (0.0786 π₯ 8.764.01) = πβπ 2,049.90 β%=
ππππππ½ππ β ππππππ·ππ (πβπ 2,049.90 β πβπ 1,900.00) πβπ 149.90 = = = π. ππ% ππππππ·ππ πβπ 1,900.00 πβπ 1,900.00
4. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in TEL stocks from December price. πΜ = πβπ 1,383.65 + 0.0315π = πβπ 1,383.65 + (0.0315 π₯ 8.764.01) = πβπ 1,659.72 β%=
ππππππ½ππ β ππππππ·ππ (πβπ 1,659.72 β πβπ 1,480.00) πβπ 179.90 = = = ππ. ππ% ππππππ·ππ πβπ 1,480.00 πβπ 1,480.00
5. By the end of October 2018, the PSEi falls at β± 7,140.29. Determine which from the two stocks has the highest percentage decrease (based on December last year prices). πΜ = πβπ 1,361.05 + 0.0786π = πβπ 1,361.05 + (0.0786 π₯ 7,140.29) = πβπ 1,922.28 β%=
ππππππππ‘ β ππππππ·ππ (πβπ 1,922.28 β πβπ 1,900.00) πβπ 22.28 = = = 1.17% ππππππ·ππ πβπ 1,900.00 πβπ 1,900.00
πΜ = πβπ 1,383.65 + 0.0315π = πβπ 1,383.65 + (0.0315 π₯ 7,140.29) = πβπ 1,608.57 β%=
ππππππππ‘ β ππππππ·ππ (πβπ 1,608.57 β πβπ 1,480.00) πβπ 128.57 = = = 8.69% ππππππ·ππ πβπ 1,480.00 πβπ 1,480.00
PLDT Stocks (TEL) will yield highest increase with 8.69% against Globe Stocks (GLO) with 1.17%
Prerequisite Activities -
Time Estimates in Weeks π‘π π‘π 2 3 2 3
π‘π 1 1
-
1
2
3
A
1
3
5
A B
1 4
4 7
13 10
B
3
6
9
D,E
5
7
9
C
2
4
6
G, I F,H,J
2 1
3 1
4 1
Required: 1. Construct the Pert network of the above activities. 2. Identify the critical path and determine the earliest completion time for the project. 3. Compute the slack time for each activity. Suggested Solution: Activities Symbol Description A Develop advertising plan B Develop the plan for promotion and advertising material C Design training programs for branch managers D Schedule advertisements (radio, TV and dailies) E Develop advertising materials F Prepare promotion material for use in in-branch promo
Prerequisite Activities -
Time Estimates in Weeks π‘π π‘π 2 3 2 3
π‘π 1 1
-
1
2
3
2
A
1
3
5
3
A B
1 4
4 7
13 10
5 7
π‘π 2 2
G H I J K
Prepare training materials for branch managers Conduct pre-introduction campaign to the media Screen and select branch managers to be trained Conduct Training program In-branch introduction of the product βESPRITβ
B
3
6
9
6
D,E
5
7
9
7
C
2
4
6
4
G, I F,H,J
2 1
3 1
4 1
3 1
1. Construct the Pert network of the above activities. 5
2 D
3
4
7
7
2
0 A
2
0
2 2
7 E
9 F
B
2
7
5
2
14
7
7
2 START
7
5
2
0
14 H
14
7
1
14
14
FINISH 15
2
3
8 G
6
5
11
9
12
J
3
11 0 C
15 K
2
2
4
4
I
2
2
14
9 7
11
2. Identify the critical path and determine the earliest completion time for the project. a. Completion Time: 15 Weeks b. Critical Path: A-E-H-K 5
2 D
3
4
7
7
2
0 A
2
0
2 2
7 E
9 F
B
2
7
5
2
14
7
7
2 START
14
7 14
14
8 G
6
5
11
9
12
J 11 0 C
2
2
4
4
9 I
2
15 K
2
3
2
7
5
2
0
14 H
7
11
3 14
1
FINISH 15
3. Compute the slack time for each activity. 5
2 D
0
2
3
4
7
7
2
0 A
0
2
0
2 2
7 E
0
2 B
3
7
2
9
14
7
5
0 14
7 14
2
8
14
G
2
11
9
12
J 2
2 C
FINISH 15
6
5
2
1
3 5
0
15 K
7
2
3
0
7
5
2
F
START
14 H
2
2
4
4
9 I
2
11
3 14
7
11
PROBLEM 2 (PERT/CPM) The following table contains information related to the major activities of a research project. Activity A B C D E F
Post β Activity C,B I D I F J
Expected Time (Days) 5 7 8 2 3 6
Required: 1. Draw the PERT/CPM network 2. Find the critical path 3. Determine the expected length of the project
Activity G H I J K
Post β Activity H K J END END
Expected Time (Days) 1 2 10 8 17
Suggested Solution: 1. Draw the PERT/CPM network 5
12 B
I
8 0
15
15
13
13
10 25
5
A
5 5
0
5 C
13
E
F
0
1
14
33
FINISH
25
3 H
1
13
25
6
19
1 G
8
9
3
19
33 J
15
3
16
25
2
13
3
0
15 D
8
5
START
25
15
7
3
20
2
K
14
17 33
16
16
2. Find the critical path Critical Path: A-C-D-I-J 5
12 B
8 0
A
15
15
13
13
10 25
5 5 5 C 5
E
13
0
1
19
1
14
3. Determine the expected length of the project Expected Length of the Project: 33 days
14
25
33
FINISH
6 25
3 H
8
9
F
1
33 J
15
3
19
25
2
13
3
16
G
15 D
8
3
0
13
I
5
0
START
25
15
7
3
2
20 K
16
16
17 33
PROBLEM 3 (PERT/CPM) Following are a set of activities for a project, their predecessor restrictions and the three time estimates of completion time. Activity A B C D E F G H I
Predecessors None None None A B B C D,E F,G,H
Optimistic 1 1 3 3 3 5 5 2 5
Most Likely 3 2 5 4 4 6 6 8 6
Pessimistic 5 3 7 5 5 13 13 14 13
Required: 1. Construct the PERT network of the above activities. 2. Identify the critical path and determine the earliest completion time for the project. 3. Compute the slack time for each activity. Suggested Solution: 1. Construct the PERT network of the above activities. Activity A B C D E F G H I
Predecessors None None None A B B C D,E F,G,H 3
0
A
Optimistic 1 1 3 3 3 5 5 2 5 3
0
3
3
7
2
6 E
B
2
3
3
2
7
15
7
8 15
4 7
2
1 START
9 F
0
5
12
G 8
22 I
15
5
5
15
7
8
C
Expected 3 2 5 4 4 7 7 8 7
4
H
0
Pessimistic 5 3 7 5 5 13 13 14 13
7
D
3
Most Likely 3 2 5 4 4 6 6 8 6
7 15
15
END
7 22
2. Identify the critical path and determine the earliest completion time for the project. Critical Path: A-D-H-I 3
0
A
3
0
7
D
3 3
4
3
7
7
15 H
2
B
2
3
3
2
15
4 7
2
1 START
9 F
0
5
22 I
15
5
5
15
7
8
C
7
6 E
0
8
END
7 22
15
12
G
7
8
15
Estimated Project Completion Time: 22 Days 3. Compute the slack time for each activity. 3
0
A
0
3 D
3
0
7
3
0
4
3
0
7
7
15 H
2 2
0 B
6 E
1
3
7
2
9
START
F
C 3
8 15
6
0 15
7
22 I
8
15
5
5
12
8
8
3 0
7
4
3
2
1
1
15
END
7 22
3
5
G
7 15
PROBLEM 4 (DECISION UNDER UNCERTAINTY) Abigail Posadas is the principal owner of Brown Oil, Inc. After quitting her university teaching job, Abi has been able to increase her annual salary by a factor of over 100. At the present time, Abi is forced to consider purchasing some more equipment for Brown Oil because of competition. Her alternatives are shown in the following table: Equipment Sub 100 Oiler J Texan
Favorable Market Php 300,000 Php 250,000 Php 75,000
Required: Under the following approaches, what would be Abiβs decision? 1. Optimistic Approach 2. Pessimistic Approach
Unfavorable Market (Php 200,000) (Php 100,000) (Php 18,000)
3. Criterion of Realism (πΌ = 0.65) 4. Equally Likely 5. Minimax Regret Suggested Solutions 1. Optimistic Approach Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
300,000.00
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
250,000.00
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
75,000.00
Choose Sub 100 as it has estimated monetary value of Php 300,000 2. Pessimistic Approach Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
(200,000.00)
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
(100,000.00)
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
(18,000.00)
Do nothing as the available options will results to net loss 3. Criterion of Realism (πΌ = 0.65) Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
125,000.00
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
127,500.00
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
42,450.00
Choose Oiler J because it has highest estimated monetary value of Php 127,500 4. Equally Likely Equipment
Favorable Market
Unfavorable Market
Payoff
Sub 100
PHP
300,000.00
PHP
(200,000.00)
PHP
50,000.00
Oiler J
PHP
250,000.00
PHP
(100,000.00)
PHP
75,000.00
Texan
PHP
75,000.00
PHP
(18,000.00)
PHP
28,500.00
5. Minimax Regret Payoff Table Equipment
Favorable Market
Unfavorable Market
Sub 100
PHP
300,000.00
PHP
(200,000.00)
Oiler J
PHP
250,000.00
PHP
(100,000.00)
Texan
PHP
75,000.00
PHP
(18,000.00)
Highest Payoff
PHP
300,000.00
PHP
(18,000.00)
Opportunity Loss Table Equipment
Favorable Market
Sub 100
PHP
Oiler J
PHP
Texan
PHP
-
Unfavorable Market
Max OL
PHP
182,000.00
PHP
182,000.00
50,000.00
PHP
82,000.00
PHP
82,000.00
225,000.00
PHP
-
PHP
225,000.00
Choose Oiler J because it has the lowest Opportunity Loss of Php 82,000 based on the table.
PROBLEM 5 (DECISION UNDER UNCERTAINTY) Todayβs Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for advising the president of Todayβs Electronics on electronic manufacturing equipment, has developed the following table concerning a proposed facility: Facility Large Medium Small No Facility
Strong Market Php 550,000 Php 300,000 Php 200,000 Php 0
Fair Market Php 110,000 Php 129,000 Php 100,000 Php 0
Required: Under the following approaches, what would be the managerβs decision? 1. 2. 3. 4. 5.
Optimistic Approach Pessimistic Approach Criterion of Realism (πΌ = 0.58) Equally Likely Minimax Regret
Poor Market (Php 310,000) (Php 100,000) (Php 32,000) Php 0
Suggested Solutions: 1. Optimistic Approach Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP
550,000.00
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP
300,000.00
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
200,000.00
No Facility
PHP
PHP
PHP
-
-
Payoff
(32,000.00) -
PHP
-
Choose to build Large Facility. 2. Pessimistic Approach Facility
Strong Market
Fair Market
Poor Market
Payoff
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP (310,000.00)
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP (100,000.00)
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
No Facility
PHP
PHP
PHP
-
-
(32,000.00) -
(32,000.00)
PHP
-
Donβt build facility. 3. Criterion of Realism (πΌ = 0.58) Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP
188,800.00
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP
132,000.00
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
102,560.00
No Facility
PHP
PHP
PHP
-
-
Payoff
(32,000.00) -
PHP
-
Choose to build Large Facility. 4. Equally Likely Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
PHP
116,666.67
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
PHP
109,666.67
Small
PHP 200,000.00
PHP 100,000.00
PHP
PHP
89,333.33
No Facility
PHP
PHP
PHP
Choose to build Large Facility.
-
-
Payoff
(32,000.00) -
PHP
-
5. Minimax Regret Payoff Table Facility
Strong Market
Fair Market
Poor Market
Large
PHP 550,000.00
PHP 110,000.00
PHP (310,000.00)
Medium
PHP 300,000.00
PHP 129,000.00
PHP (100,000.00)
Small
PHP 200,000.00
PHP 100,000.00
PHP
No Facility
PHP
PHP
-
PHP
-
Highest Payoff
PHP 550,000.00
PHP 129,000.00
PHP
-
-
(32,000.00)
Opportunity Loss Table Facility
Strong Market
Fair Market
Poor Market
Max OL
Large
PHP
-
PHP
19,000.00
PHP
310,000.00
PHP
310,000.00
Medium
PHP 250,000.00
PHP
-
PHP
100,000.00
PHP
250,000.00
Small
PHP 350,000.00
PHP
29,000.00
PHP
32,000.00
PHP
350,000.00
No Facility
PHP 550,000.00
PHP 129,000.00
PHP
PHP
550,000.00
-
Choose to build Medium Facility PROBLEM 6 (DECISION UNDER RISK) A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (i.e., there is a favorable market for the clinic), the physicians could realize a net profit of Php 10,000,000. If the market is not favorable, they could lose Php 400,000. Of course, they donβt have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50β50 chance the clinic will be successful. Required: Construct a decision tree to help analyze this problem. What should the medical professionals do? Suggested Solutions:
Php 0
Do Nothing EMV = Php 0
Php 10,000,000 Favorable Market (50%) EMV = Php 10,000,000 x 50% = Php 5,000,000 Construct a Clinic EMV = Php 4,200,000
Unfavorable Market (50%) Php (400,000) EMV = Php (400,000) x 50% = Php (200,000) Build a clinic as it will give the medical profession an estimated monetary value of Php 4,200,000. PROBLEM 7 (DECISION UNDER RISK) The physicians in Problem 6 have been approached by a market research firm that offers to perform a study of the market at a fee of Php 50,000. The market researchers claim their experience enables them to use Bayesβ theorem to make the following statements of probability: Probability Favorable Market Unfavorable Market
Favorable Study 82% 18%
Unfavorable Study 11% 89%
The probability that the outcome of a favorable study is 55%, while unfavorable study would results to 45% probability.
Php 9,950,000 Favorable Market (82%) EMV = Php 9,950,000 x 82% = Php 8,159,000 Build a Clinic
EMV = Php 8,078,000
Unfavorable Market (18%) EMV = Php 8,078,000
Php (450,000) EMV = Php (450,000) x 18% = Php (81,000) Do Not Build a Clinic
Php (50,000)
Favorable Survey (55%) EMV = Php 8,078,000 x 55% = Php 4,447,850
EMV = Php 9,950,000 x 11% = Php 1,094,500 Php 9,950,000
Favorable Market (11%)
EMV = Php 694,000 x 45% = Php 312,300 EMV = Php 694,000 Unfavorable Survey (45%) Build a Clinic Conduct Market Survey Unfavorable Market (89%) EMV = Php 4,760,150 EMV = Php 694,000
Php (450,000) EMV = Php (450,000) x 89% = Php (400,500)
Do Not Build a Clinic Php (50,000) EMV = Php 10,000,000 x 50% = Php 5,000,000 Php 10,000,000 Favorable Market (50%) Do Not Conduct Market Survey
EMV = Php 4,200,000
EMV = Php 4,200,000 Build a Clinic Unfavorable Market (50%) EMV = Php 4,200,000
Php (400,000) EMV = Php (400,000) x 50% = Php (200,000)
Do Not Build a Clinic Php 0
The decision should be to conduct a survey and in either results of the survey, build a clinic.
PROBLEM 8 (REGRESSION ANALYSIS) Vianne Jane Ibarreta runs a florist shop on the Quezon City, specializing in floral arrangements for weddings and other special events. She advertises weekly in the local newspapers and is considering increasing her advertising budget. Before doing so, she decides to evaluate the past effectiveness of these ads. Five weeks are sampled, and the advertising peso and sales volume for each of these is shown in the following table. Advertising Php 5,000 Php 3,000 Php 7,000 Php 2,000 Php 8,000
Sales Php 11,000 Php 6,000 Php 10,000 Php 6,000 Php 12,000
Required: a. b. c. d. e.
Determine the mean of the dependent variable. Determine the mean of the independent variable. Determine the regression line. If Vianne decided to shell out Php 12,000 in advertising expense, what would be her expected sales? If Vianne wants to have sales of Php 15,000, based on the regression line, how much advertising expense should be budget?
Suggested Solutions: a. Determine the mean of the dependent variable. Dependent variable is Sales b. Determine the mean of the independent variable. Independent variable is Advertising Expenses c. Determine the regression line. πΏ 5,000 3,000 7,000 2,000 8,000 βπ = 25,000 25,000 πΜ = = 5,000 5 π1 =
π 11,000 6,000 10,000 6,000 12,000 βπ = 45,000 45,000 πΜ = = 9,000 5
Μ ) (πΏ β πΏ 0 (2,000) 2,000 (3,000) 3,000
β(π β πΜ )(π β πΜ ) 26,000,000 = = 1.00 β(π β πΜ )2 26,000,000
Μ ) (π β π 2,000 (3,000) 1,000 (3,000) 3,000
Μ )π (πΏ β πΏ 0 4,000,000 4,000,000 9,000,000 9,000,000 β = 26,000,000
Μ )(π β π Μ ) (πΏ β πΏ 0 6,000,000 2,000,000 9,000,000 9,000,000 β = 26,000,000
π0 = πΜ β π1 πΜ = 9,000 β (1.000)5,000 = 4,000
Μ = π·ππ π, πππ + πΏ π d. If Vianne decided to shell out Php 12,000 in advertising expense, what would be her expected sales? πΜ = πβπ 4,000 + π = πβπ 4,000 + 12,000 = πβπ 4,000 + πβπ 12,000 = π·ππ ππ, πππ
e. If Vianne wants to have sales of Php 15,000, based on the regression line, how much advertising expense should be budget? πΜ = πβπ 4,000 + π = πβπ 4,000 + 15,000 = πβπ 4,000 + πβπ 15,000 = π·ππ ππ, πππ PROBLEM 9 (REGRESSION ANALYSIS) Chino PateΓ±o is a real estate broker, he was able to gather the following data (selling price, square footage, number of bedrooms, and age of houses) that have sold in a neighborhood in the past 6 months. Selling Price Php 6,400,000 Php 5,900,000 Php 6,150,000 Php 7,900,000 Php 8,750,000 Php 9,250,000 Php 9,500,000 Php 11,300,000 Php 11,500,000 Php 13,800,000 Php 14,250,000 Php 14,400,000 Php 14,500,000 Php 14,750,000 Php 14,400,000 Php 15,550,000 Php 16,500,000
Square Foot 1,670 1,339 1,712 1,840 2,300 2,234 2,311 2,377 2,736 2,500 2,500 2,479 2,400 3,124 2,500 4,062 2,854
No. of Bedrooms 2 2 3 3 3 3 3 3 4 3 4 3 3 4 3 4 3
Age (In Years) 30 25 30 40 18 30 19 7 10 1 3 3 1 0 2 10 3
Required: 1. 2. 3. 4. 5.
What is the regression line if you want to determine the sales price using square foot? What is the regression line if you want to determine the sales price using no. of bedrooms? What is the regression line if you want to determine the sales price using age in years? What would be the selling price of a unit with 2,789 square foot? If a client has a budget of Php 10,000,000. What is the average years of the house should Chino suggest?
Suggested Solutions: 1. What is the regression line if you want to determine the sales price using square foot? πΏ
π
1,670 1,339 1,712 1,840 2,300 2,234 2,311 2,377 2,736 2,500 2,500
6,400,000 5,900,000 6,150,000 7,900,000 8,750,000 9,250,000 9,500,000 11,300,000 11,500,000 13,800,000 14,250,000
Μ ) (πΏ β πΏ (738.12) (1,069.12) (696.12) (568.12) (108.12) (174.12) (97.12) (31.12) 327.88 91.88 91.88
Μ ) (π β π
Μ )π (πΏ β πΏ
(5,058,823.53) (5,558,823.53) (5,308,823.53) (3,558,823.53) (2,708,823.53) (2,208,823.53) (1,958,823.53) (158,823.53) 41,176.47 2,341,176.47 2,791,176.47
544,817.66 1,143,012.54 484,579.78 322,757.66 11,689.43 30,316.96 9,431.84 968.31 107,506.84 8,442.37 8,442.37
Μ )(π β π Μ ) (πΏ β πΏ 3,734,006,920.42 5,943,036,332.18 3,695,565,743.94 2,021,830,449.83 292,871,626.30 384,595,155.71 190,236,332.18 4,942,214.53 13,501,038.06 215,112,802.77 256,459,861.59
2,479 2,400 3,124 2,500 4,062 2,854 βπ = 40,938 40,938 πΜ = 17 = 2,408.12
π1 =
14,400,000 14,500,000 14,750,000 14,400,000 15,550,000 16,500,000 βπ = 194,800,000 194,800,000 πΜ = 17 = 11,458,823.53
70.88 (8.12) 715.88 91.88 1,653.88 445.88
2,941,176.47 3,041,176.47 3,291,176.47 2,941,176.47 4,091,176.47 5,041,176.47
5,024.31 65.90 512,487.54 8,442.37 2,735,326.84 198,811.07
208,477,508.65 (24,687,197.23) 2,356,095,155.71 270,242,214.53 6,766,324,567.47 2,247,771,626.30
β = 6,132,123.76
β = 28,576,382,352.94
β(π β πΜ )(π β πΜ ) 28,576,382,352.94 = = 4,660.11 β(π β πΜ )2 6,132,123.76
π0 = πΜ β π1 πΜ = 11,458,823.53 β (4,660.11)2,408.12 = 236,719.45 Μ = π·ππ πππ, πππ. ππ + π, πππ. πππΏ π 2. What is the regression line if you want to determine the sales price using no. of bedrooms? πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
2 2 3 3 3 3 3 3 4 3 4 3 3 4 3 4 3 βπ = 53
6,400,000 5,900,000 6,150,000 7,900,000 8,750,000 9,250,000 9,500,000 11,300,000 11,500,000 13,800,000 14,250,000 14,400,000 14,500,000 14,750,000 14,400,000 15,550,000 16,500,000 βπ = 194,800,000
(738.12) (1,069.12) (696.12) (568.12) (108.12) (174.12) (97.12) (31.12) 327.88 91.88 91.88 70.88 (8.12) 715.88 91.88 1,653.88 445.88
(5,058,823.53) (5,558,823.53) (5,308,823.53) (3,558,823.53) (2,708,823.53) (2,208,823.53) (1,958,823.53) (158,823.53) 41,176.47 2,341,176.47 2,791,176.47 2,941,176.47 3,041,176.47 3,291,176.47 2,941,176.47 4,091,176.47 5,041,176.47
1.25 1.25 0.01 0.01 0.01 0.01 0.01 0.01 0.78 0.01 0.78 0.01 0.01 0.78 0.01 0.78
53 17 = 3.12 πΜ =
π1 =
0.01 β = 5,76
194,800,000 17 = 11,458,823.53 πΜ =
β(π β πΜ )(π β πΜ ) 20,832,352.94 = = 3,616,727.94 β(π β πΜ )2 5.76
π0 = πΜ β π1 πΜ = 11,458,823.53 β (3,616,727.94)3.12 = 174,632.36 Μ = π·ππ πππ, πππ. ππ + π, πππ, πππ. πππΏ π
Μ )(π β π Μ ) (πΏ β πΏ 5,653,979.24 6,212,802.77 624,567.47 418,685.12 318,685.12 259,861.59 230,449.83 18,685.12 36,332.18 (275,432.53) 2,462,802.77 (346,020.76) (357,785.47) 2,903,979.24 (346,020.76) 3,609,861.59 (593,079.58) β = 20,832,352.94
3. What is the regression line if you want to determine the sales price using age in years? πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
Μ )(π β π Μ ) (πΏ β πΏ
30 25 30 40 18 30 19 7 10 1 3 3 1 0 2 10 3 βπ = 232
6,400,000 5,900,000 6,150,000 7,900,000 8,750,000 9,250,000 9,500,000 11,300,000 11,500,000 13,800,000 14,250,000 14,400,000 14,500,000 14,750,000 14,400,000 15,550,000 16,500,000 βπ = 194,800,000
16.35 11.35 16.35 26.35 4.35 16.35 5.35 (6.65) (3.65) (12.65) (10.65) (10.65) (12.65) (13.65) (11.65) (3.65) (10.65)
(5,058,823.53) (5,558,823.53) (5,308,823.53) (3,558,823.53) (2,708,823.53) (2,208,823.53) (1,958,823.53) (158,823.53) 41,176.47 2,341,176.47 2,791,176.47 2,941,176.47 3,041,176.47 3,291,176.47 2,941,176.47 4,091,176.47 5,041,176.47
267.42 128.89 267.42 694.48 18.95 267.42 28.65 44.18 13.30 159.95 113.36 113.36 159.95 186.24 135.65 13.30 113.36
(82,726,643.60) (63,108,996.54) (86,814,878.89) (93,785,467.13) (11,791,349.48) (36,120,761.25) (10,485,467.13) 1,055,709.34 (150,173.01) (29,608,996.54) (29,717,820.07) (31,314,878.89) (38,461,937.72) (44,914,878.89) (34,256,055.36) (14,920,761.25) (53,673,702.42)
β = 2,725.88
β = (660,797,058.82)
232 17 = 13.65 πΜ =
π1 =
194,800,000 17 = 11,458,823.53 πΜ =
β(π β πΜ )(π β πΜ ) (660,797,058.82) = = (242,416.05) β(π β πΜ )2 2,725.88
π0 = πΜ β π1 πΜ = 11,458,823.53 β (β242,416.05)13.65 = 14,767,802.61 Μ = π·ππ ππ, πππ, πππ. ππ β πππ, πππ. πππΏ π 4. What would be the selling price of a unit with 2,789 square foot? πΜ = πβπ 236,719.45 + 4,660.11π = πβπ 236,719.45 + (4,660.11)(2,789) = π·ππ ππ, πππ, πππ. ππ 5. If a client has a budget of 10,000,000. What is the average years of the house should Chino suggest? πΜ = πβπ 14,767,802.61 β 242,416.05π β π =
π=
πβπ 14,767,802.61 β πΜ 242,416.05
14,767,802.61 β 10,000,000 4,767,802.61 = = ππ. ππ ππ¬π¨πΉπΊ 242,416.05 242,416.05
PROBLEM 10 (REGRESSION ANALYSIS) The closing stock price of Globe and PLDT was recorded over a 12-month period in 2017. The closing price for the Philippine Stocks Exchange Index (PSEi) was also recorded over this same time period. These values are shown in the following table: Month January February March April May June July August September October November December
β± β± β± β± β± β± β± β± β± β± β± β±
PSEi 7,229.66 7,212.09 7,311.72 7,661.01 7,837.12 7,843.16 8,018.05 7,958.57 8,171.43 8,365.26 8,254.03 8,558.42
β± β± β± β± β± β± β± β± β± β± β± β±
Globe (GLO) 1,720.00 1,828.00 2,032.00 2,078.00 2,110.00 2,048.00 2,116.00 2,000.00 2,050.00 2,042.00 1,830.00 1,900.00
β± β± β± β± β± β± β± β± β± β± β± β±
PLDT (TEL) 1,470.00 1,460.00 1,646.00 1,770.00 1,728.00 1,798.00 1,637.00 1,730.00 1,668.00 1,710.00 1,481.00 1,480.00
Required: 1. Based on the PSEi prices, determine the regression line of GLO stocks. 2. Based on the PSEi prices, determine the regression line of TEL stocks. 3. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in GLO stocks from December price. 4. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in TEL stocks from December price. 5. By the end of October 2018, the PSEi falls at β± 7,140.29. Determine which from the two stocks has the highest percentage decrease. Suggested Solutions 1. Based on the PSEi prices, determine the regression line of GLO stocks. πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
Μ )(π β π Μ ) (πΏ β πΏ
7,229.66 7,212.09 7,311.72 7,661.01 7,837.12 7,843.16 8,018.05 7,958.57 8,171.43 8,365.26 8,254.03 8,558.42 βπ = 94,420.52
1,720.00 1,828.00 2,032.00 2,078.00 2,110.00 2,048.00 2,116.00 2,000.00 2,050.00 2,042.00 1,830.00 1,900.00 βπ = 23,754.00
(638.72) (656.29) (556.66) (207.37) (31.26) (25.22) 149.67 90.19 303.05 496.88 385.65 690.04
(259.50) (151.50) 52.50 98.50 130.50 68.50 136.50 20.50 70.50 62.50 (149.50) (79.50)
407,958.98 430,712.19 309,866.64 43,000.93 976.98 635.88 22,402.11 8,134.84 91,841.32 246,893.05 148,728.49 476,159.80 β = 2,187,311.22
165,746.98 99,427.43 (29,224.48) (20,425.62) (4,079.00) (1,727.34) 20,430.41 1,848.96 21,365.26 31,055.21 (57,655.17) (54,858.45) β = 171,904.20
94,420.52 12 = 7,868.38 πΜ =
23,754.00 12 = 1,979.50 πΜ =
π1 =
β(π β πΜ )(π β πΜ ) 171,904.20 = = 0.0786 2 β(π β πΜ ) 2,187,311.22
π0 = πΜ β π1 πΜ = 1,979.50 β (0.0786)7,868.38 = 1,361.05 Μ = π·ππ π, πππ. ππ + π. πππππΏ π 2. Based on the PSEi prices, determine the regression line of TEL stocks. πΏ
π
Μ ) (πΏ β πΏ
Μ ) (π β π
Μ )π (πΏ β πΏ
Μ )(π β π Μ ) (πΏ β πΏ
7,229.66 7,212.09 7,311.72 7,661.01 7,837.12 7,843.16 8,018.05 7,958.57 8,171.43 8,365.26 8,254.03 8,558.42 βπ = 94,420.52
1,470.00 1,460.00 1,646.00 1,770.00 1,728.00 1,798.00 1,637.00 1,730.00 1,668.00 1,710.00 1,481.00 1,480.00 βπ = 19,578.00
(638.72) (656.29) (556.66) (207.37) (31.26) (25.22) 149.67 90.19 303.05 496.88 385.65 690.04
(161.50) (171.50) 14.50 138.50 96.50 166.50 5.50 98.50 36.50 78.50 (150.50) (151.50)
26,082.25 29,412.25 210.25 19,182.25 9,312.25 27,722.25 30.25 9,702.25 1,332.25 6,162.25 22,650.25 22,952.25 β = 2,187,311.22
103,152.74 112,553.16 (8,071.52) (28,720.28) (3,016.27) (4,198.58) 823.20 8,884.04 11,061.45 39,005.34 (58,040.83) (104,541.57) β = 68,890.90
94,420.52 12 = 7,868.38 πΜ =
π1 =
19,578.00 12 = 1,631.50 πΜ =
β(π β πΜ )(π β πΜ ) 68,890.90 = = 0.0315 2 β(π β πΜ ) 2,187,311.22
π0 = πΜ β π1 πΜ = 1,631.50 β (0.0315)7,868.38 = 1,383.65 Μ = π·ππ π, πππ. ππ + π. πππππΏ π
3. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in GLO stocks from December price. πΜ = πβπ 1,361.05 + 0.0786π = πβπ 1,361.05 + (0.0786 π₯ 8.764.01) = πβπ 2,049.90 β%=
ππππππ½ππ β ππππππ·ππ (πβπ 2,049.90 β πβπ 1,900.00) πβπ 149.90 = = = π. ππ% ππππππ·ππ πβπ 1,900.00 πβπ 1,900.00
4. On January 2018, the closing price of PSEi was at β± 8,764.01. Determine the percentage increase or decrease in TEL stocks from December price. πΜ = πβπ 1,383.65 + 0.0315π = πβπ 1,383.65 + (0.0315 π₯ 8.764.01) = πβπ 1,659.72 β%=
ππππππ½ππ β ππππππ·ππ (πβπ 1,659.72 β πβπ 1,480.00) πβπ 179.90 = = = ππ. ππ% ππππππ·ππ πβπ 1,480.00 πβπ 1,480.00
5. By the end of October 2018, the PSEi falls at β± 7,140.29. Determine which from the two stocks has the highest percentage decrease (based on December last year prices). πΜ = πβπ 1,361.05 + 0.0786π = πβπ 1,361.05 + (0.0786 π₯ 7,140.29) = πβπ 1,922.28 β%=
ππππππππ‘ β ππππππ·ππ (πβπ 1,922.28 β πβπ 1,900.00) πβπ 22.28 = = = 1.17% ππππππ·ππ πβπ 1,900.00 πβπ 1,900.00
πΜ = πβπ 1,383.65 + 0.0315π = πβπ 1,383.65 + (0.0315 π₯ 7,140.29) = πβπ 1,608.57 β%=
ππππππππ‘ β ππππππ·ππ (πβπ 1,608.57 β πβπ 1,480.00) πβπ 128.57 = = = 8.69% ππππππ·ππ πβπ 1,480.00 πβπ 1,480.00
PLDT Stocks (TEL) will yield highest increase with 8.69% against Globe Stocks (GLO) with 1.17%
Related Documents
Mas
August 2019 56
Mas
November 2019 51
Mas
November 2019 50
Mas
October 2019 52
Mas
May 2020 24
Mas
May 2020 25More Documents from ""
Iac-stockholders-students (1).docx
August 2019 46
Mas
August 2019 56
Powerbuilder-acceder A Un Servidor
November 2019 32
Portales Cms
November 2019 45
Php - Flash
November 2019 48