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 $1,700, and the cost required to set up the production line for the 6-cylinder connecting rods is $4,000. Manufacturing costs are $14 for each 4-cylinder connecting rod and $24 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 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 are 5,300 6-cylinder connecting rods and 7,300 4-cylinder connecting rods.

Let
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

Problem 7-09 (Algorithmic) produce the Hawkins Manufacturing Company produces con necting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line 4-cylinder connecting rods is $1,700, and the cost required to set up the production line for the 6-cylinder connecting rods is $4,000. Manufacturing costs are $14 for each 4-cylinder connecting rod and $24 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 a production changeover is necessary from one week the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,300 6-cylinder connecting rods and 7,300 4-cylinder connecting rods. Let 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 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise $6 a. Using the decision variables x4 and s4, write constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7,300 units. x4 SA b. Using the decision variables x6 and S6, write constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5,300 units. XE 56 c. Write three constraints that, taken together, limit the production of connecting rods for next week X4 54 x6 S6 S4+ S6 d. Write an objective function for minimizing the cost production for next week. Min x4 x6 $4 S6

Answer 1

a. X₄ $\leq$ 7300 S₄

b. X₆ $\leq$ 5300 S6

c. X₄ $\leq$ 7300 S₄

X₆ $\leq$ 5300 S₆

S₄ + S₆ = 1