*5. In a 3 X 3 transportation problem, let Xij be the amount shipped from source i to destination j and let Cij be the corresponding transportation cost per unit. The amounts of supply at sources 1,2, and 3 are 15,30, and 85 units, respectively, and the demands at destinations 1,2, and 3 are 20,30, and 80 units, respectively. Assume that the starting northwest-corner solution is optimal and that the associated values of the multipliers are given as UI = -2, U2 = 3, U3 = 5, VI = 2, Vz = 5, and V3 = 10.

(a) Find the associated optimal cost.

(b) Determine the smallest value of Gij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.