# Linear Programming Concepts, shadow price and sensitivity

What does the shadow price reflect in a maximization problem? explain.

How do the graphical and computer-based methods of solving LP problems differ? In what ways are they the same? Under what circumstances would you prefer to use the graphical approach? How does sensitivity analysis affect the decision making process? How could it be used by managers?

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Linear programming/Sensitivity Analysis

What does the shadow price reflect in a maximization problem? explain.

In the context of a maximization problem with a constraint, the shadow price on the constrain is the amount that the objective function of the maximization would increase by if the constraint were relaxed by one unit (Econterms, 2012).

The concept is briefly described as "a shadow price is the maximum price that management is willing to pay for an extra unit of a given limited resource. For example, if a production line is already operating at its maximum 40 hour limit, the shadow price would be the maximum price the manager would be willing to pay for operating it for an additional hour, based on the benefits he would get from this change" (Answers.com, 2012).

Other references would show that "the value of the shadow price can provide decision makers powerful insight into problems. For instance if you have a constraint that limits the amount of labor available to 40 hours per week, the shadow price will tell you how much you would be willing to pay for an additional hour of labor. If your shadow price is $10 for the labor constraint, for instance, you should pay no more than $10 an hour for additional labor. Labor costs of less than $10/hour will increase the objective value; labor costs of more than $10/hour will decrease the objective value. Labor ...

#### Solution Summary

This solution discusses the concepts of shadow price and maximization problem, differences between graphical and computer-based methods of solving LP problems differ, and sensitivity analysis in decision making process.