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# In a 3 x 3 transportation problem, let xij be the amount shipped from source i...

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 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 cij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.

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