Question

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 $1,800, and the cost required to set up the productlon line for the 6-cylinder connecting rods is $3,100. Manufacturing costs are $13 for each 4-cylinder connecting rod and each week as to which product will be manufactured the following week. If a production changeover is necessary from $25 for each 6-cylinder connecting rod. Hawkins makes decision at the end 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 5,100 6-cylinder connecting rods and 7,200 4-cylinder connecting rods. Let X4 the number of 4-cylinder connecting rods produced next week X6 = the number f 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 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise s6 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 7,200 units. X4 S S4 b. Using the decision varlables x6 and s6, write a constraint that limits next week's production of the 6-cylinder connecting rods to elther 0 or 5,100 units. x6 S connecting rods for next week. c. Write three constraints that, taken together, limit the production x4 S Se Se S4 d. Write an objective function for minimizing the cost of production for next week Min X4 + X6 + S4 S6

Answer 1

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 7,200 units. 1X4 7200 S4 b. Using the decision varlables x6 and s6, write a constraint that llmits next week's production of the 6-cyllnder connecting rods to elther 0 or 5,100 unlts. 5100 c. Write three constraints that, taken together, limit the production of cannecting rods for next week. 7200 4 1 X4 S 5100 S6 1 6 S 1541S6 1 d. Write an objective function for minimizing the cost of production for next week. Min 13 X4 25 X6 1800 543100s6