MANUFACTURING
Response to the following problem:
Plant Equipment Corporation (PEC) manufactures two large industrial machines-a metal compactor and a drill press. Next month PEC will convert its production facilities to produce new machine designs and will cease producing the current models. PEC must determine its production schedule for this month, however. PEC could sell up to three compactors and two drill presses to customers who are not anxious to pay the increased price PEC will charge for the new models. Current models net PEC a $24,000 profit for metal compactors and $30,000 for drill presses. Each metal compactor requires 50 hours to produce, whereas each drill press requires 60 hours to produce; 160 production hours are available during the current month.
a. Formulate and solve this problem as an integer linear programming problem.
b. Solve the problem as a linear program and note that when the optimal solution is rounded (up, down, or off), the result is not the optimal integer solution.
c. Why would a linear programming model be a correct model if the production process were to continue indefinitely?