What is dual of a Linear Program?

During a lecture, some of the students were not clear about why do we think about the dual of a Linear Program and how this can be useful in various applications. Here some of the points are listed for ready reference:

1: With every linear program, there is a dual program associated. The relationship of dual variables with the values in the optimal primal table gives lot of useful information that can be used in decision making. If these features are build in the Business Intelligence Software, it can bring decison makers closer to decision.

2: If we maximize something say, profit in a product mix problem, we try to find out how much of different products should be produced under the constraints posed by availability of resources and demands so that the profit is maximum. When we solve this problem and move towards optimality, we are simultaneously minimizing the profit generating capability of the remaining resources. Thus another linear program which is actually a minimization problem is also getting solved simultaneously when we are solving the maximization problem. These problems are dual to each other.

3: Identifying the dual program is easy and the techniques are discussed in any book on OR. So, interested students can take help from there. But, if you find any difficulty, please get in touch by writing comment or at the contact detail available on the page.

4: Optimal solution of the primal problem gives solution of the dual problem as well. And this relationship can be used in making many decisions. To list a few:
... It can be used in finding out the resources that should be given priority in buying if additional fund is available.
... It can be used in deciding about the training priorities for different people.
... It can also be used in prioritizing the areas for technical improvements and so on.

You use your innovativeness and you can see that it can provide a useful tool in helping scientifc decision making in various areas. Some peoblems for practice will be posted soon.