9. Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automo- bile 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 pro- duction 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 de- cision 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 re- configure the production line. Once the line has been set up, the weekly production capaci- ties are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Let Problems 513 xu = the number of 4-cylinder connecting rods produced next week Xo = 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 $6 = 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 54, write a constraint that limits next week's pro- duction of the 4-cylinder connecting rods to either 0 or 8000 units. b. Using the decision variables x, and so, write a constraint that limits next week's pro- duction of the 6-cylinder connecting rods to either 0 or 6000 units. c. Write three constraints that, taken together, limit the production of connecting rods for next week. d. Write an objective function for minimizing the cost of production for next week