Hawkins manufacturing Company produces connection 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 $2000, and the cost required to set up the production line for the 6- cylinder connecting rods is $3500. 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 there is a production changeover 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 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Let

= the number of 4-cylinder connecting rods produced next week

= the number of 6-cylinder connecting rods produced next week

= 1 if the production line is set up to produce the 4-cylinder connecting

rods 0 otherwise

= 1 if the production line is set up to produce the 6-cylinder connecting

rods 0 otherwise

a. Using the decision variables and write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8000 units

b. Using the dicision variables and , write a constraint that limest next weeks production of the 6-cylinder connectiong rods to either 0 or 8000 units.

c. Write three constraints that, taken together, limit the production of connecting rods for next week.

= the number of 4-cylinder connecting rods produced next week

= the number of 6-cylinder connecting rods produced next week

= 1 if the production line is set up to produce the 4-cylinder connecting

rods 0 otherwise

= 1 if the production line is set up to produce the 6-cylinder connecting

rods 0 otherwise

a. Using the decision variables and write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 8000 units

b. Using the dicision variables and , write a constraint that limest next weeks production of the 6-cylinder connectiong rods to either 0 or 8000 units.

c. Write three constraints that, taken together, limit the production of connecting rods for next week.

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