An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 27

Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder auto mobile 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. It 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 arc 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Let
x 4 = the number of 4-cylinder connecting rods produced next week
x 6 = the number of 6-cylinder connecting rods produced next week
S 4 = 1 if the production line is set up to produce the 4-cylinder connecting rods: 0 if otherwise
S 6 = 1 if the production line is set up to produce the 6-cylinder connecting rods: 0 if otherwise
a. Using the decision variables x 4 and x 4 , 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 x 6 and x 6 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 rode for next week.
d. Write an objective function for minimizing the cost of production for next week.