Consider the LP Maximizez CX subjectto AX b, X 0, where b 0 After obtaining the optimum solution, it is suggested that a nonbasic variable x j can be made basic (profitable) by reducing the resource requirements per unit of x j to 1 of their original values, 1 Since the requirements per unit are reduced, it is expected that the profit per unit of x j will also be reduced to 1 of its original value Will these changes make x j a profitable variable Explain mathematically

Question: Consider the LP Maximizez = CX subjectto AX b, X 0, where b 0 After obtaining the optimum solution, it is suggested

Consider the LP Maximizez = CX subjectto AX ≤ b, X ≥ 0, where b ≥ 0 After obtaining the optimum solution, it is suggested that a nonbasic variable x_jcan be made basic (profitable) by reducing the resource requirements per unit of x_j to 1/α of their original values, α > 1. Since the requirements per unit are reduced, it is expected that the profit per unit of x_j will also be reduced to 1/α of its original value. Will these changes make x_j a profitable variable? Explain mathematically.

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