Consider the Following Linear Programming Problem

question 48

Short Answer

Consider the following linear programming problem:
Max Z =    5x1 + 3x2
Subject to:    6x1 + 2x2 ? 18
      15x1 + 20x2 ? 60
      x1 , x2 ? 0
Find the optimal profit and the values of x1 and x2 at the optimal solution.

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Definitions:

Constant Returns to Scale

A situation where increasing all inputs by a certain factor results in output increasing by the same factor, indicating proportionate scalability of production.

Increasing Returns to Scale

Occurs when an increase in all inputs by a certain percentage causes a more than proportional increase in output.

Decreasing Returns to Scale

Decreasing returns to scale occur when an increase in all inputs leads to a less than proportional increase in output, showing that the firm becomes less efficient as it scales up production.

Increasing Opportunity Costs

A situation where the cost of forgoing the next best alternative increases as more resources are devoted to an activity.