old_prelim3 - OR&IE 320/520 Old Prelim #3...

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Unformatted text preview: OR&IE 320/520 Old Prelim #3 Questions 1. Suppose you are given a transportation problem with the following data (supplies a i , demands b j , unit shipping costs c ij ): Supplies 2 3 11 7 6 1 6 1 2 5 7 15 9 9 Demands 7 5 3 2 (a) (6) Find an initial basic feasible solution and indicate a tree which corresponds to it. (b) (6) Show that x 12 = 5 , x 13 = 1 , x 23 = 2 , x 31 = 7 , x 34 = 2 is an optimal solution by constructing a dual feasible solution which is complementary to this solution. (c) (6) Determine a basis which corresponds to the optimal (primal) solution from part (b). Is the basis unique? Why? (d) (12) Suppose that u 1 , u 2 , u 3 , v 1 , v 2 , v 3 , v 4 is a feasible dual solution for this problem. Show that if the (same) value is added to each u i and subtracted from each v j the resulting solution remains dual feasible. (e) (10) Determine an optimal solution to the dual problem for which all dual variables corresponding to demand nodes (the v j values) are negative ....
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old_prelim3 - OR&IE 320/520 Old Prelim #3...

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