Operation Research -3

SHRI V.K. PANDE COLLEGE OF SCIENCE AND MANAGEMENT HINGANGHAT SESSIONAL EXAMINATION -2009 BACHELOR OF COMPUTER APPLICATION-I SUBJECT :OPERATION RESEARCH-3 TIME:- THREE HOURS MARKS:-40 N.B 1:- All questions are compulsory and carry equal marks 2:- Draw neat diagram wherever necessary. EITHER: (4*2) 1. A) Write short note on the following:i. Origin and Development of OR ii. Methodogies in OR iii. Nature of OR iv. OR Model. B) Formulate the LPP Model and Solve By Graphical Method. Chairs Tables (Per table) (PerChair Hours Profit ) Available Contributi 7 5 on Carpentry 3Hrs 4Hrs 2400 Painting

2Hrs

1Hrs

Other Limitations: • Make no more than 450 chairs • Make at least 100 tables

1000 OR

C) i) Write a one line Dafination on the following term:i. Optimal solution ii. Unbounded solution iii. Infesible solution solution iv. Degenerate solution with finite vi. Unbounded solution space ii) Formulation of Duality Problem and Explain it application. D) Solve by simplex method Consider Z = 3x + 5y EITHER: Sources

W1 F1 10 Factory F2 70 F3 40 Requirments 5

Subject to x < 40, y < 30, x + y < 60, x, y > 0. (4*2)

W2 30 30 8 8

Wahrehouse W3 50 40 70 7

W4 10 60 20 14

Capacity 7 9 18 34

B) Explain the zero one model for assignment problem with example. OR

C) What is Game Theory? Explain its Terminologies. D) Solve the follwing 3x5 game using dominance property:Player B Strategy 1 2 3 4 1 6 15 30 21 Player 2 3 3 6 6 A 3 12 12 24 36

5 6 4 3

EITHER: (4*2) 3. A) Explain the various quantitive (criterion)methods which are usful for decision making under Uncertinity and Risk. B) Given below is a payoff Table:Event (State of Nature) Action

E1

E2

E3

E4

A1

50

300

-150

50

A2

400

0

100

0

A3

-50

200

0

100

A4

0

300

300

Indicate decision taken under the following approaches. i. Pessimistic ii. Optimistic iii. Laplace Crite iv.Suppose that the probabilites of the evnts in this are ; P(E1)=0.15 P(E2)=0.45; P(E3)=0.25; P(E4)=0.1 Calculate EMV AND EOL

0 OR

C) The details of a project consisting of activities A to K are summarized in Table.

Activity

Immediat e Predeces sor(s)

Duration (Weeks)

to tm tp A 6 7 8 1. Construct the project diagram B 1 2 9 2. Find the Expected duration and C 1 4 7 the variance of each activity D A 1 2 3 3. Find the critical path and Project E A,B 1 2 9 expected completion time. F C 1 5 9 G C 2 2 8 H E,F 4 4 4 I E,F 4 4 10 J D,H 2 5 14 K I,G 2 2 8 D) Explain the following term: i. Basic conept of network ii. Time cost Trade OFF aspects in N iii. Constraints in Network iv. Advantage in Network EITHER: (4*2) 4 A) Name and Types of models of inventory system and explain tham in detail. B) i)The demand for a purchased item is 1000 units per month and the shrotage are allowed if the unit cost if the unit cost is Rs.15 per unit,the cost of making one purchases is Rs.600, the holding cost for 1 unit is Rs.20 per year and the cost of one shortage is Rs. 100 per year determine. a. Economic order quantity b. The optimum number of Shortage c. The time between orders d. The number of orders per year e. The optimum annual cost.

ii) if the items can be manufactured at a rate of 4000 per month. If all the costs are the same. Determin f. The optimum quantity of manufactures g. The optimum number of shortage h. The optimal annual cost i. The time of shortage j. The time between setup k.The time to manufacture optimum quantity OR

C) Write short note on:- 1. Inventory control 2. Inventory Costs 3. Types of Inventory 4. Inventory Objective. D) A contractor of second hand motor trucks maintains a stock of trucks. Every month demand of the trucks occurs at a relatively constant rate but not in a constant size. The demand is show in the following

probability distribution:Demand 0 1 2 3 4 5 6 or more Probabiltiy 0.4 0.24 0.20 0.10 0.05 0.01 0.00 the holding cost of an old truck in stock for one month is Rs.100 and the penalty for a truck if not supplied on demand is Rs.1000.00. Determine the optimal size of the stock of the contractor? EITHER: (4*2) 5 A) Write a short note on:- 1. Queueing system 2. Transient and steady state B) Vehicles are passing through a toll gate at the rate of 70 per hour. The average time to pass through the gate is 45 seconds. The arrival rate and service rate follows possion distribution there is a complaint that the vehicles wait for long duration the authorites are willing to instal one more gate to reduce the average time to pass through the toll gate to 35 seconds of the idle time of the tol gate is less then 9% and the average queue length at the gate is more than 8 vehicles check whether the installation of the second gate is justified.

OR C) List and explain the terminologies used in queueing system. D) In a supermarket the average arrival rate of customer is 10 every 30 minutes follwing possion process The average time taken by a cashier to lost and calculate the customer is 2.5 minutes following exponential distribution. What is the probability that the queue length excceds 6 ? What is the expected time spent by a customer in the system?