For a linear programming problem where the decision variables are not required to take integer values, the optimal solutions will occur at one or more of the extreme points, i.e. vertices of the feasible region. The method of solution is to calculate the value of the objective function at each vertex, and the maximum or minimum (as required) of these values identifies any optimal solutions. Where more than one such vertex is found, all points on the boundary of the feasible region between them will also be an optimal solution. Compare simplex method.