Linear Programming: Production Problem
A manufacturing company produces four different models of integrated circuits. Each type of circuit requires material, labor, and machine time.
The optimal combination of the four types of circuits is limited by the constraints of availability for these three resources. The formulation of the linear programming production problem is:
Maximize Z = 12x1 + 10x2 + 15x3 + 11x4 (objective function for profit)
Subject to the following constraints:
| Material: |
5x1 + 3x2 + 4x3 + 2x4 <= 240 pounds |
| Machine time: |
6x1 + 8x2 + 2x3 + 3x4 <= 240 hours |
| Labor: |
2x1 + 3x2 + 3x3 + 2x4 <= 180 hours |
Nonnegativity: x1, x2, x3, x4 >= 0
Where: x1 = quantity of Product 1 produced
x2 = quantity of Product 2 produced
x3 = quantity of Product 3 produced
x4 = quantity of Product 4 produced
Use Microsoft Excel and Solver to find the optimal solution for the production problem. Be sure that values selected by the computer are integers (as it doesn't make any sense to discuss producing part of a unit of a product).
Include your interpretation of the results by stating:
How many of each product will be produced?
What is the profit for the optimal solution?
What resource(s) is limiting the production?