Hawkins 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 $1,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,100. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 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 6,500 6-cylinder connecting rods and 8,200 4-cylinder connecting rods. Let x4 = the number of 4-cylinder connecting rods produced next week X6 = the number of 6-cylinder connecting rods produced next week S4= 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise S6 = 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 s4, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8,200 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". X4 54 b. Using the decision variables xs and s6, write a constraint that limits next week's production of the 6-cylinder connecting rods to either O or 6,500 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". X6 c. Write three constraints that, taken together, limit the production of connecting rods for next week. If the constant is "1" it must be entered in the box. If your answer is zero enter "o". X4 54 X6 56
Hawkins 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 $1,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,100. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 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 6,500 6-cylinder connecting rods and 8,200 4-cylinder connecting rods. Let x4 = the number of 4-cylinder connecting rods produced next week X6 = the number of 6-cylinder connecting rods produced next week S4= 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise S6 = 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 s4, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8,200 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". X4 54 b. Using the decision variables xs and s6, write a constraint that limits next week's production of the 6-cylinder connecting rods to either O or 6,500 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". X6 c. Write three constraints that, taken together, limit the production of connecting rods for next week. If the constant is "1" it must be entered in the box. If your answer is zero enter "o". X4 54 X6 56
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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**Problem 7-09 (Algorithmic)**
Hawkins 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 $1,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,100. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 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 6,500 6-cylinder connecting rods and 8,200 4-cylinder connecting rods.
Let:
- \( x_4 \) = the number of 4-cylinder connecting rods produced next week
- \( x_6 \) = the number of 6-cylinder connecting rods produced next week
- \( s_4 \) = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise
- \( s_6 \) = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise
**a.** Using the decision variables \( x_4 \) and \( s_4 \), write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8,200 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0".
- \[ \text{[Answer Box] } x_4 \leq \text{[Answer Box] } s_4 \]
**b.** Using the decision variables \( x_6 \) and \( s_6 \), write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 6,500 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0".
- \[ \text{[Answer Box] } x_6 \leq \text{[Answer Box] } s](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7730b928-1739-40db-bc3b-b66e677f8a3a%2Fdb89293d-d7cd-40a2-a9e0-eaed7e9f8f15%2Faj36uhfv_processed.png&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcribed text suitable for an educational website:
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**Problem 7-09 (Algorithmic)**
Hawkins 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 $1,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,100. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 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 6,500 6-cylinder connecting rods and 8,200 4-cylinder connecting rods.
Let:
- \( x_4 \) = the number of 4-cylinder connecting rods produced next week
- \( x_6 \) = the number of 6-cylinder connecting rods produced next week
- \( s_4 \) = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise
- \( s_6 \) = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise
**a.** Using the decision variables \( x_4 \) and \( s_4 \), write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8,200 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0".
- \[ \text{[Answer Box] } x_4 \leq \text{[Answer Box] } s_4 \]
**b.** Using the decision variables \( x_6 \) and \( s_6 \), write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 6,500 units. If the constant is "1" it must be entered in the box. If your answer is zero enter "0".
- \[ \text{[Answer Box] } x_6 \leq \text{[Answer Box] } s
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