Homework Chapter 4+5+6 Ncu
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Chapter 4+5+6 . HOMEWORK Part A . Break-Even Revenue . 1. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 85 x − 2004 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 2. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 82 x − 2004 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 3. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 84 x − 2001 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even .
4. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 80 x − 2001 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even .
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5. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 85 x − 2002 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 6. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 84 x − 2002 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 7. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 80 x − 2003 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 8. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 82 x − 2003 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . --------------------------------------------------------------------------------------
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Part B . Average Cost of Production . 1. * The average cost per unit for the production of LG Televisions is given by 5004 + 82 x + x 2 C ( x) = , where x is the number of hundreds of units x produced . Find x to get the average cost that is at most $590 per unit . 2. * The average cost per unit for the production of LG Televisions is given by 5002 + 80 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $580 per unit . 3. * The average cost per unit for the production of LG Televisions is given by 5000 + 80 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $590 per unit . 4. * The average cost per unit for the production of LG Televisions is given by 5000 + 82 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $580 per unit . 5. * The average cost per unit for the production of LG Televisions is given by
4
5004 + 80 x + x 2 C ( x) = x
,
where x is the number of hundreds of units
produced . Find x to get the average cost that is at most $580 per unit . 6. * The average cost per unit for the production of LG Televisions is given by 5002 + 82 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $560 per unit . 7. * The average cost per unit for the production of LG Televisions is given by 5002 + 82 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $590 per unit . 8. * The average cost per unit for the production of LG Televisions is given by 5002 + 80 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $560 per unit . --------------------------------------------------------------------------------------
5
Part C : Revenue – Cost – Profit 1.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $274000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 25 20 32 ( cubic ft ) Weights 25 36 66 ( pounds ) Value 160 180 290 ( dollars ) 2.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 24 22 28 ( cubic ft ) Weights 22 36 68 ( pounds ) Value 140 190 280 ( dollars ) 3.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the
6
products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 20 24 36 ( cubic ft ) Weights 20 36 66 ( pounds ) Value 170 190 290 ( dollars ) 4.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 26 20 28 ( cubic ft ) Weights 22 34 66 ( pounds ) Value 140 190 320 ( dollars ) 5.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 22 26 32 ( cubic ft ) Weights 24 34 68
7
( pounds ) Value ( dollars )
160
170
290
6.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 26 22 28 ( cubic ft ) Weights 24 36 66 ( pounds ) Value 140 170 320 ( dollars ) 7.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 24 20 32 ( cubic ft ) Weights 20 32 68 ( pounds ) Value 140 160 320 ( dollars )
8.* Transportation .
8
Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 22 26 32 ( cubic ft ) Weights 26 36 68 ( pounds ) Value 160 190 320 ( dollars )
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Part D : LINEAR PROGRAMMING .
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1.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 62 units of S -model and 78 units of P -model per hour . Plant 2 can assemble 290 units of S -model and 90 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 2.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 60 units of S -model and 82 units of P -model per hour . Plant 2 can assemble 310 units of S -model and 70 units of P -model per hour . The company needs to product at least 5400 units of S –model and 3800 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 3.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 64 units of S -model and 76 units of P -model per hour . Plant 2 can assemble 280 units of S -model and 100 units of P -model per hour . The company needs to product at least 5600 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ?
10
4.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 68 units of S -model and 76 units of P -model per hour . Plant 2 can assemble 310 units of S -model and 70 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 5.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 50 units of S -model and 90 units of P -model per hour . Plant 2 can assemble 280 units of S -model and 100 units of P -model per hour . The company needs to product at least 5600 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 6.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 70 units of S -model and 70 units of P -model per hour . Plant 2 can assemble 320 units of S -model and 60 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4000 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 7.* Cost Minimization .
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The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 64 units of S -model and 78 units of P -model per hour . Plant 2 can assemble 280 units of S -model and 90 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 8.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 66 units of S -model and 76 units of P -model per hour . Plant 2 can assemble 320 units of S -model and 60 units of P -model per hour . The company needs to product at least 5000 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ?
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Part E : LINEAR PROGRAMMING .
12
1 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.3 pound of beef and 0.2 pound of spices . The company has at most 1010 pounds of beef and at most 510 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
2 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.7 pound of beef and 0.3 pound of spices and each pound of regular hot dog requires 0.4 pound of beef and 0.1 pound of spices . The company has at most 1000 pounds of beef and at most 520 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
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3 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.4 pound of beef and 0.2 pound of spices . The company has at most 1020 pounds of beef and at most 510 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
4 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.7 pound of beef and 0.3 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.2 pound of spices . The company has at most 1040 pounds of beef and at most 520 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
5 .* Maximizing Profit :
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The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.3 pound of spices . The company has at most 1020 pounds of beef and at most 500 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
6 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.3 pound of spices . The company has at most 1010 pounds of beef and at most 520 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
7 .* Maximizing Profit :
15
The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.7 pound of beef and 0.3 pound of spices and each pound of regular hot dog requires 0.6 pound of beef and 0.2 pound of spices . The company has at most 1000 pounds of beef and at most 540 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
8 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.8 pound of beef and 0.2 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.2 pound of spices . The company has at most 1000 pounds of beef and at most 540 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
HOMEWORK
Class :
Members :
S.ID :
16
SPRING SEMESTER 2008
1. 2. 3. 4.
Chapter : 4 + 5 + 6
Part Part Part Part
A: B: C: D:
Date :
www.hotchalk.com
Classcode : 3KIOMNW17
TOTAL SCORES
Chapter 4+5+6 . HOMEWORK Part A . Break-Even Revenue . 1. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 85 x − 2004 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 2. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 82 x − 2004 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 3. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 84 x − 2001 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even .
4. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 80 x − 2001 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even .
2
5. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 85 x − 2002 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 6. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 84 x − 2002 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 7. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 11x 2 − 80 x − 2003 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . 8. Cubic Functions : The weekly profit for a product is P ( x ) = −0.1x 3 + 12 x 2 − 82 x − 2003 ( thousand dollars ) , where x is the number of thousand of units produced and sold . To find the number of units that gives break-even : a. Graph the profit function and find x-intercepts of the graph . b. Determine the levels of production that give break-even . --------------------------------------------------------------------------------------
3
Part B . Average Cost of Production . 1. * The average cost per unit for the production of LG Televisions is given by 5004 + 82 x + x 2 C ( x) = , where x is the number of hundreds of units x produced . Find x to get the average cost that is at most $590 per unit . 2. * The average cost per unit for the production of LG Televisions is given by 5002 + 80 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $580 per unit . 3. * The average cost per unit for the production of LG Televisions is given by 5000 + 80 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $590 per unit . 4. * The average cost per unit for the production of LG Televisions is given by 5000 + 82 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $580 per unit . 5. * The average cost per unit for the production of LG Televisions is given by
4
5004 + 80 x + x 2 C ( x) = x
,
where x is the number of hundreds of units
produced . Find x to get the average cost that is at most $580 per unit . 6. * The average cost per unit for the production of LG Televisions is given by 5002 + 82 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $560 per unit . 7. * The average cost per unit for the production of LG Televisions is given by 5002 + 82 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $590 per unit . 8. * The average cost per unit for the production of LG Televisions is given by 5002 + 80 x + x 2 , where x is the number of hundreds of units C ( x) = x produced . Find x to get the average cost that is at most $560 per unit . --------------------------------------------------------------------------------------
5
Part C : Revenue – Cost – Profit 1.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $274000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 25 20 32 ( cubic ft ) Weights 25 36 66 ( pounds ) Value 160 180 290 ( dollars ) 2.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 24 22 28 ( cubic ft ) Weights 22 36 68 ( pounds ) Value 140 190 280 ( dollars ) 3.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the
6
products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 20 24 36 ( cubic ft ) Weights 20 36 66 ( pounds ) Value 170 190 290 ( dollars ) 4.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 26 20 28 ( cubic ft ) Weights 22 34 66 ( pounds ) Value 140 190 320 ( dollars ) 5.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 22 26 32 ( cubic ft ) Weights 24 34 68
7
( pounds ) Value ( dollars )
160
170
290
6.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 26 22 28 ( cubic ft ) Weights 24 36 66 ( pounds ) Value 140 170 320 ( dollars ) 7.* Transportation . Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 24 20 32 ( cubic ft ) Weights 20 32 68 ( pounds ) Value 140 160 320 ( dollars )
8.* Transportation .
8
Ace Trucking Company has an order for 3 products A , B and C for delivery . The table below gives the volumn in cubic feet , the weight in pounds and the value for insurance in dollars for a unit of each of the products . If the company can carry 30,000 cubic feet and 62,000 lb and is insured for $276000 , how many units of each product can be carried? A (x) B (y) C (z) Unit Volumn 22 26 32 ( cubic ft ) Weights 26 36 68 ( pounds ) Value 160 190 320 ( dollars )
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Part D : LINEAR PROGRAMMING .
9
1.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 62 units of S -model and 78 units of P -model per hour . Plant 2 can assemble 290 units of S -model and 90 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 2.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 60 units of S -model and 82 units of P -model per hour . Plant 2 can assemble 310 units of S -model and 70 units of P -model per hour . The company needs to product at least 5400 units of S –model and 3800 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 3.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 64 units of S -model and 76 units of P -model per hour . Plant 2 can assemble 280 units of S -model and 100 units of P -model per hour . The company needs to product at least 5600 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ?
10
4.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 68 units of S -model and 76 units of P -model per hour . Plant 2 can assemble 310 units of S -model and 70 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 5.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 50 units of S -model and 90 units of P -model per hour . Plant 2 can assemble 280 units of S -model and 100 units of P -model per hour . The company needs to product at least 5600 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 6.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 70 units of S -model and 70 units of P -model per hour . Plant 2 can assemble 320 units of S -model and 60 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4000 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 7.* Cost Minimization .
11
The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 64 units of S -model and 78 units of P -model per hour . Plant 2 can assemble 280 units of S -model and 90 units of P -model per hour . The company needs to product at least 5200 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ? 8.* Cost Minimization . The Star Company produces 2 types of DVD players , which are assembled at 2 different locations . Plant 1 can assemble 66 units of S -model and 76 units of P -model per hour . Plant 2 can assemble 320 units of S -model and 60 units of P -model per hour . The company needs to product at least 5000 units of S –model and 4200 units of P –model to fill an order . If it costs $2000/h to run Plant 1 and $3000/h to run Plant 2 How many hours should each plant spend on manufacturing DVD players to minimize its cost for this order ? What is the minimum cost for this order ?
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Part E : LINEAR PROGRAMMING .
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1 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.3 pound of beef and 0.2 pound of spices . The company has at most 1010 pounds of beef and at most 510 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
2 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.7 pound of beef and 0.3 pound of spices and each pound of regular hot dog requires 0.4 pound of beef and 0.1 pound of spices . The company has at most 1000 pounds of beef and at most 520 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
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3 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.4 pound of beef and 0.2 pound of spices . The company has at most 1020 pounds of beef and at most 510 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
4 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.7 pound of beef and 0.3 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.2 pound of spices . The company has at most 1040 pounds of beef and at most 520 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
5 .* Maximizing Profit :
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The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.3 pound of spices . The company has at most 1020 pounds of beef and at most 500 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
6 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.6 pound of beef and 0.4 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.3 pound of spices . The company has at most 1010 pounds of beef and at most 520 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
7 .* Maximizing Profit :
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The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.7 pound of beef and 0.3 pound of spices and each pound of regular hot dog requires 0.6 pound of beef and 0.2 pound of spices . The company has at most 1000 pounds of beef and at most 540 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
8 .* Maximizing Profit : The Smoker Meat Packing makes 2 different types of hotdogs , regular and all-beef . Each pound of all-beef hot dogs requires 0.8 pound of beef and 0.2 pound of spices and each pound of regular hot dog requires 0.5 pound of beef and 0.2 pound of spices . The company has at most 1000 pounds of beef and at most 540 pounds of spices for hot dogs . If the profit is $0.90 on each pound of all-beef and $1.20 on each pound of regular hot dogs , how many of each type should be produced to maximize the profit ? Solution : All-beef (x) Regular (y) Beef Total beef Spices Total spices Profit Profit P
HOMEWORK
Class :
Members :
S.ID :
16
SPRING SEMESTER 2008
1. 2. 3. 4.
Chapter : 4 + 5 + 6
Part Part Part Part
A: B: C: D:
Date :
www.hotchalk.com
Classcode : 3KIOMNW17
TOTAL SCORES
