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 $1800, and the cost required to set up the production line for the 6-cylinder connecting rods is $3300. Manufacturing costs are $15 for each 4-cylinder connecting rod and $20 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 6200 6-cylinder connecting rods and 8400 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 8400 units.
   
   x₄s₄
   
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 6200 units.
   
   x₆s₆
   
3. Write three constraints that, taken together, limit the production of connecting rods for next week.
   
   x₄s₄
   
   x₆s₆
   
   s₄ + s₆
   
4. Write an objective function for minimizing the cost of production for next week.
   
   Min x₄ + x₆ + s₄ + s₆

Answer 1