12. Consider the LP Maximize z = ex subject to AX $ b, X ;;:::: 0, where...
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12. Consider the LP Maximize z = ex subject to AX $
b, X ;;:::: 0, where b ;;:::: 0 After obtaining the optimum solution, it is suggested that a nonbasic variable Xi can be made basic (profitable) by reducing the (resource) requirements per unit of Xi for the different resources to ~ of their original values, a > 1. Since the requirements per unit are reduced, it is expected that the profit per unit of Xj will also be reduced to ±of its original value. Will these changes make Xj a profitable variable? Explain mathematically.
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