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 roads 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 roads produced next week x6 = the number of 6 cylinder connecting roads 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 3 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