Status Resources

We had classified constraints as scarce and abundant, depending respectively on whether or not the optimum solution "consumes" the entire available amount of the associated resource. Our objective is to secure the information from the optimum tableau. First we must clarify one point. Speaking of resources implies that there is a maximum limit on its availability, which means that the constraint must originally be of type ≤. Thus constraints of the type ≥ cannot physically represent a resource restriction; rather, they imply that the solution must meet certain requirements, such as satisfying minimum demand or minimum specifications.

In our problem we have four constraints of the type ≤. The first two (representing raw materials usage) are "authentic" resource restrictions. The third and fourth constraints deal with demand limitations imposed by the market conditions. We can think of these constraints as limited "resources", since increasing demand limits is equivalent to expanding the company's share in the market.  Monetarily, this has the same effect as increasing availability of physical resources (such as raw materials) through allocation of additional funds.  Following the discussion above, the status of resources (abundant or scarce) in any LP model can be secured directly from the optimum tableau by observing the values of the slack variables.