Question

In a 3 x 3 transportation problem, let x_ij be the amount shipped from source i to destination j, and let c_ij 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 assosciated values of the multipliers are given as u₁ = -2, u2 = 3, u3 = 5, v₁ = 2, v₃ = 5, and v₃ = 10. Find the assosciated optimal cost, and determine the smallest value of c_ij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.

Answer 1