Consider the problem Minimize z = a m i=1 a n j=1 cij xij subject to a n j=1 xij ai, i = 1,

Consider the problem Minimize z = a m i=1 a n j=1 cij xij subject to a n j=1 xij Ú ai, i = 1, 2,c, m a m i=1 xij Ú bj, j = 1, 2,c, n xij Ú 0, all i and j It may appear logical to assume that the optimum solution will require the first (second) set of inequalities to be replaced with equations if Σai Ú Σbj 1Σai … Σbj2.
The counterexample in Table 5.38 shows that this assumption is not correct.
Show that the application of the suggested procedure yields the solution x11 = 2, x12 = 3, x22 = 4, and x23 = 2, with z = $27, which is worse than the feasible solution x11 = 2, x12 = 7, and x23 = 6, with z = $15.