The transportation problem in Table 5.37 gives the indicated degenerate basic solution

(i.e., at least one of the basic variables is zero). Suppose that the multipliers associated with this solution are u1 = 1, u2 = -1, v 1 = 2, v 2 = 2, and v 3 = 5 and that the unit cost for all (basic and nonbasic) zero xij variables is given by cij = i + ju, - ∞ 6 u 6 ∞

(a) If the given solution is optimal, determine the associated optimal value of the objective function.

(b) Determine the value of u that will guarantee the optimality of the given solution.

(Hint: Locate the zero basic variable.)