Suppose that separable programming has been applied to a certain problem (the "original problem") to convert it to the following equivalent linear programming model in algebraic form:

Maximize Profit = 5X₁₁ + 4X₁₂ + 2X₁₃ + 4X₂₁ + X₂₂

subject to

3X₁₁ + 3X₁₂ + 3X₁₃ + 2X₂₁ + 2X₂₂ 25

2X₁₁ + 2X₁₂ + 2X₁₃ - X₂₁ - X₂₂ 10

and

0 X₁₁ 2 0 X₂₁ 3

0 X₁₂ 3 0 X₂₂ 1

0 X₁₃

What was the mathematical model for the original problem? Answer this by plotting the profit graph for each of the original activities and the writing the constraints for the original problem in terms of the original decision variables.

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