Explore BrainMass

Explore BrainMass

    Linear Programming for Integrated Circuits

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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).

    © BrainMass Inc. brainmass.com June 4, 2020, 4:12 am ad1c9bdddf
    https://brainmass.com/business/business-management/linear-programming-for-integrated-circuits-550354

    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.

    $2.19

    ADVERTISEMENT