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Linear Programming for Integrated Circuits

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).

Solution Preview

Given data:

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

Steps using solver:

1. Rearrange the data.
...

Solution Summary

This is a linear programming problems using a combination of given inputs such as machine time, and labor to optimally produce integrated circuits 1, 2, 3, and 4. The computation utilized Excel Solver. The step-by-step solution is provided in the attached file.

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