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/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.