Inequality Constraints

Many production or resource constraints faced by managers are inequalities. Constraints often limit the resource employed to less than or equal to (<) some fixed amount available. In other instances, constraints specify that the quantity or quality of output must be greater than or equal to (>) some minimum requirement. Linear programming handles such constraint inequalities easily, making it a useful technique for finding the optimal solution to many management decision problems.

A typical linear programming problem might be to maximize output subject to the constraint that no more than 40 hours of skilled labor per week be used. This labor constraint is expressed as an inequality where skilled labor < 40 hours per week. Such an operating constraint means that no more than 40 hours of skilled labor can be used, but some excess capacity is permissible, at least in the short run. If 36 hours of skilled labor were fruitfully employed during a given week, the 4 hours per week of unused labor is called excess capacity.

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