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 $1800, and the cost required to set up the production line for the 6-cylinder connecting rods is $3200. Manufacturing costs are $13 for each 4-cylinder connecting rod and $20 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 5500 6-cylinder connecting rods and 7600 4-cylinder connecting rods. L

et

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

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 7600 units.

________x4 _______ ________s4

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 5500 units.

_____ x6 ________ ________ s6

Write three constraints that, taken together, limit the production of connecting rods for next week.

_______ x4 _____ ________ s4

_______ x6 _______ ______s6

________s4 + ________ s6 ______ ______

Write an objective function for minimizing the cost of production for next week.

Min________x4 + _______ x6 + _________ s4 + ________ s6