This Demonstration illustrates the graphical solution to several linear programming problems, all of which have the same set of constraints; you can vary the objective function. When two corner points are optimal, so are all the points on the line segment connecting them. The region shaded in blue is the feasible region and the colored lines correspond to the constraints. The black line represents the chosen objective function set to the slider value.
In this Demonstration, it is not possible to choose an objective function that makes optimal because such an objective function would either involve a minimization problem or a maximization problem with negative coefficients for and . Such problems would require different values for the right hand side and so do not fit well with the slider. You cannot make and optimal because such an objective function would be a vertical line.