The values of the optimal dual variables have an interesting economic interpretation. To see this, let's assume for instance that the primal problem describes a production problem in which the objective function represents the gain one obtains from the production of n goods, while the constraints represent bounds on the production amounts due to the presence of limited resources. The avaible quantity of each resource i is measured by the component b(i) of the vector b. Suppose now that the manager of the production is
willing to invest in buying new resources in order to augment the production and thus his gain. How much must he be ready to pay for an additional unit of resource i in order to increase its net gain? Obviously the price he pays for each unit of resource should not be greater than the increment in the gain that it produces. So the question becomes: How much does the optimal value of the problem increase when we augment each resource i? Let's see how to answer this problem.