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 rod is $2,000, and the cost required to set up the production for the 6-cylinder connecting rod is $3,500. 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 a production changeover is necessary from one week to the next, the weekend is used to recongure the production line. Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 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 and =0 otherwise, s6 = 1 if the production line is set up to produce the 6-cylinder connecting
rods and =0 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 8,000 units.
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 6,000 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.