# Linear Programming Technique:

After studying this chapter you should be able to:

## Definition and Explanation:

Linear programming is a mathematical technique which permits determination of the best use of available resources.

It is a valuable aid to management because it provides a systematic and efficient procedure which can be used as a guide in decision making. The heart of management’s responsibility is the best or optimum use of limited resources that include money, personnel, materials, facilities, and time.

The contribution margin is one measure of whether management is making the best use of resources. When the total contribution margin is maximized, management’s profit objective should be satisfied. Click here to read full article.

Simplex method is considered one of the basic techniques from which many linear programming techniques are directly or indirectly derived. The simplex method is an iterative, stepwise process which approaches an optimum solution in order to reach an objective function of maximization or minimization. Click here to read full article.

Graphical method can be applied to minimization problems in the same manner as illustrated on maximization example page. An example can make the concept clear. Click here to read full article

The determination of the optimum mix to maximize the contribution margin or to minimize cost assumes a defined set of constraints. It is useful to consider the sensitivity of the solution if a constraint is relaxed.  This effect is often referred to as shadow price and simply shows the change in contribution margin (in a contribution margin maximization problem) or the change in cost (in a cost minimization problem) resulting from relaxing a constraint. Click here to read full article.

Dynamic programming is an extension of the basic linear programming technique and involves breaking the problem into a set of smaller problems and then reassembling the results of the analysis. Click here to read full article.

The maximization and minimization studies, together with the exercises and presented in this section, are realistic examples of the types of problems management faces. By maximizing certain managerial objectives such as contribution margin and utilization of available labor hours or factory capacity, or by minimizing functions such as cost, weight, materials mix, or time, management’s goal can be determined quantitatively. Click here to read full article.