Minimizing the cost of production for next week

Question

Case Scenario:

Hawkins manufacturing Company produces connection 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 $2000, and the cost required to set up the production line for the 6- cylinder connecting rods is $3500. Manufacturing costs are $15 for each 4- cylinder connecting rod and $18 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 6000 6-cylinder connecting rods and 8000 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 otherwise

S₆ = 1 if the production line is set up to produce the 6-cylinder connecting  rods 0 otherwise

Question 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 8000 units

Question 2: Using the dicision variables X₆ and S₆, write a constraint that limest next weeks production of the 6-cylinder connectiong rods to either 0 or 8000 units.

Question 3: Write three constraints that, taken together, limit the production of connecting rods for next week.

Question 4: Write an objective function for minimizing the cost of production for next week.