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 $1,700, and the cost required to set up the production line for the 6-cylinder connecting rods is $4,000. Manufacturing costs are $14 for each 4-cylinder connecting rod and $24 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 5,300 6-cylinder connecting rods and 7,300 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 constraint that limits next week's production of the 4-cylinder connecting rods too either 0 or 7,300 units. 7300 1 x4 S S4 b. Using the decision variables x6 and s6, write constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5,300 units. 5300 x6 S SE c. Write three constraints that, taken together, limit the production of connecting rods for next week. X4 S 7200 S4 5300 x6 S S6 S4+ S6 d. Write an objective function for minimizing the cost of production for next week Min S4 + X4 SE + 9x