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 $1800, and the cost required to set up the production line for the 6-cylinder connecting rods is $3800. Manufacturing costs are $14 for each 4-cylinder connecting rod and $20 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 5900 6-cylinder connecting rods and 7900 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 7900 units.

____________x4 is what comapred to ____________s4

(B) Using the decision variables x₆ and s₆, write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5900 units.

____________x6 is what comapred to ____________s6

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

____________x4 is what comapred to ____________s4

____________x6 is what comapred to ____________s6

____________s4 is what comapred to ____________s6 = ____________

(D) Write an objective function for minimizing the cost of production for next week.

MIN ____________x4 + ____________ x6 + ____________s4 + ____________s6