Consider the Following Linear Programming Problem

question 88

Essay

Consider the following linear programming problem:
MIN Z =    3x1 + 2x2
Subject to:    2x1 + 3x2 ? 12
    5x1 + 8x2 ? 37
    x1, x2 ? 0
At the optimal solution point, the objective function value is 18. If the constraints are changed from greater than to less than constraints and the objective function is changed from minimize to maximize, what happens to the optimal solution? Demonstrate whether it falls at the same optimal point.

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Definitions:

Fixed-Coefficient Technology

A production process where input ratios are constant and cannot be substituted for one another in the production process.

Demand Function

A mathematical relationship that describes how the quantity demanded of a good or service varies with changes in its price, and possibly other factors.

Horizontal Labor Supply Curve

A graphical representation suggesting that a worker's willingness to work does not change regardless of wage increases over a certain range.

Monopolist

A single seller in a market who has significant control over the price and supply of a product or service.