Having built a linear programming model we should be very careful before we rely too heavily on the answers it produces. Once a model has been built and converted into the format necessary for the computer program we will wish to attempt to solve it. Assuming that there are no obvious clerical or keying errors (which are usually detected by package programs) there are three possible outcomes: (i) the model is infeasible; (ii) the model is unbounded; (iii) the model is solvable.
A linear programming model is infeasible if the constraints are self-contradictory. For example, a model which contained the following two constraints would be infeasible:
In practice, the infeasibility would probably be more disguised (unless it arose through a simple keying error). The program will probably go some way towards trying to solve the model until it detects that it is infeasible. Most package programs will print out the infeasible solution obtained at the point when the program gives up.
In most situations an infeasible model indicates an error in the mathematical formulation of the problem. It is, of course, possible that we are trying to devise some plan that is ...