Problem 11-9 (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 $2000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3400. Manufacturing costs are $13 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 6300 6-cylinder connecting rods and 7800 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 7800 units. X4 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 6300 units. X6 S6 c. Write three constraints that, taken together, limit the production of connecting rods for next week. X4 S4