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Reduced cost isSelect one:a. Non-zero for basic variable and zero for non-basic variableb. Zero for basic variable and non-zero for non-basic variablec. Zero for both basic and non-basic variabled. Non-zero for both basic and non-basic variable

Question

Reduced cost isSelect one:a. Non-zero for basic variable and zero for non-basic variableb. Zero for basic variable and non-zero for non-basic variablec. Zero for both basic and non-basic variabled. Non-zero for both basic and non-basic variable

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Solution

The correct answer is b. Zero for basic variable and non-zero for non-basic variable.

In linear programming, the reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (increase for a maximization problem, decrease for a minimization problem) before it would be possible for a corresponding non-basic variable to enter the solution mix.

So, for basic variables (those included in the solution), the reduced cost is zero because they are already in the solution mix. For non-basic variables (those not in the solution), the reduced cost is non-zero because it represents the improvement needed for them to enter the solution mix.

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