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Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let x₁ = the number of 4-cylinder connecting rods produced next week x6 = the number of 6-cylinder connecting rods produced next week S = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise S = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x and s, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7,000 units. (b) Using the decision variables x, and so write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5,000 units. (c) Write a third constraint that, taken with the constraints from parts (a) and (b), limits the production of connecting rods for next week. (d) Write an objective function for minimizing the cost of production for next week. Min

Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let x₁ = the number of 4-cylinder connecting rods produced next week x6 = the number of 6-cylinder connecting rods produced next week S = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise S = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x and s, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7,000 units. (b) Using the decision variables x, and so write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5,000 units. (c) Write a third constraint that, taken with the constraints from parts (a) and (b), limits the production of connecting rods for next week. (d) Write an objective function for minimizing the cost of production for next week. Min

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let 56 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x4 and s, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7,000 units. хо (b) Using the decision variables x, and s, write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5,000 units. 10 X4 = the number of 4-cylinder connecting rods produced next week Min X6 = the number of 6-cylinder connecting rods produced next week (c) Write a third constraint that, taken with the constraints from parts (a) and (b), limits the production of connecting rods for next week. S4 = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise (d) Write an objective function for minimizing the cost of production for next week. Type here to search 2 1 3 E MANCA 100 X 4 11 R F5 de 5 % ☀ + T F6 6 LO 1 Y F7 W & 7 ✈ X F8 U 8 J F10 ( 75°F F11 V (8) + 11 7:10 PM 3/4/2024 8 PRE
Transcribed Image Text:Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let 56 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x4 and s, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7,000 units. хо (b) Using the decision variables x, and s, write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5,000 units. 10 X4 = the number of 4-cylinder connecting rods produced next week Min X6 = the number of 6-cylinder connecting rods produced next week (c) Write a third constraint that, taken with the constraints from parts (a) and (b), limits the production of connecting rods for next week. S4 = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise (d) Write an objective function for minimizing the cost of production for next week. Type here to search 2 1 3 E MANCA 100 X 4 11 R F5 de 5 % ☀ + T F6 6 LO 1 Y F7 W & 7 ✈ X F8 U 8 J F10 ( 75°F F11 V (8) + 11 7:10 PM 3/4/2024 8 PRE
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