Hawkins Manufacturing Company produces connecting rods for 4 and 6-cylinder auto- mobile engines using the same production line. The cost required to...

Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines...

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 productionline to produce the 4—cylinder connecting rods is $2000, and the cost required to set up theproduction line for the l6-cylinder connecting rods is $3500. Manufacturing costs are $15for each 4—cylinder connecting rod and $18 for each 6—cylinder connecting rod. Hawkinsmakes a decision at the end of each week as to which product will be manufactured thefollowing week. If 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, theweekly production capacities are 6000 6-cylinder connecting rods and 8000 4—cylinderconnecting rods. Let M = the number of 4-cylinder connecting rods produced next weekx6 = 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 .95 = 1 if the production line is set up to produce the 6-cylinder connecting rods;0 if otherwise 21. Using the decision variables x4 and S4, write a constraint that limits next week’s produc—tion of the 4—cylinder connecting rods to either 0 or 8000 units. 1}. Using the decision variables x6 and 36, write a constraint that limits next week’s produc—tion 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 fornext week. (1. Write an objective function for minimizing the cost of production for next week.