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 $3500. 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 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 6000 6-cylinder connecting rods and 8000 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 8000 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 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.