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Unformatted text preview: x 1 , x 5 non basic at the upper bound, s the slack variable is basic. (c). Solve using the Simplex method with upper bounds, starting from the tableau in part (b). (d). Now consider the general (fractional) knapsack problem: max z = c 1 x 1 + . . . + c n x n a 1 x 1 + . . . + a n x n b x 1 , . . . , x n 1 where c i > 0, a i > 0 for i = 1 , . . . , n and b > 0. Show that for all such knapsack problems, there exists an optimal solution in which at most one of the variables is non integer. Hint: Consider BFS. (e). Suggest a simple way to solve the problem in part (d) (without using simplex)....
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- Fall '08
- Linear Programming