Problem 11-9 (Algorithmic)

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 $2100, and the cost required to set up the production line for the 6-cylinder connecting rods is $3300. Manufacturing costs are $16 for each 4-cylinder connecting rod and $19 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 5600 6-cylinder connecting rods and 8100 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

1. 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 8100 units. fill in the blank 1x₄fill in the blank 3s₄
2. 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 5600 units. fill in the blank 4x₆fill in the blank 6s₆
3. Write three constraints that, taken together, limit the production of connecting rods for next week. fill in the blank 7x₄fill in the blank 9s₄ fill in the blank 10x₆fill in the blank 12s₆ fill in the blank 13s₄ + fill in the blank 14s₆fill in the blank 16
4. Write an objective function for minimizing the cost of production for next week. Min fill in the blank 17x₄ + fill in the blank 18x₆ + fill in the blank 19s₄ + fill in the blank 20s₆