The minimum of the cost equation is $64. This is equal to the maximum of the profit equation (see Example: Primal Problem). This will always be true; at the optimum solution, the primal objective function value will equal the dual objective function value. Table 1 gives the optimal solution, since no variables have nega-tive values. u 1 has a value of $8, u2 and u3 both equal zero, and u4 has a value of $18.