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5 - APM236 HW5 due Wed March 16 NAME Consider the following...

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Unformatted text preview: APM236 HW5 due Wed. March 16 NAME: Consider the following information about a LPP in the canonical format: 3 2 1 −1 0 0 1 2 1 2 0 , b = 4 , c = A= 3 0 2 0 1 −3 0 1 0 3 1 −1 2 −1 2 Assume that the initial basic variables were x1 , x4 and x2 in this order, and that at this stage the present basic variables are x3 , x4 and x2 in this order. a) By looking at the information and without any operations present the matrix B that is responsible for this stage of the operation. (present your reasoing.) b) Determine B −1 by row reduction. c) Use your B −1 and the rest of the information to compute the solution and the objective value. Determine if the solution is optimal. Page 1 of 3 APM236 HW5 due Wed. March 16 NAME: d) If the solution is optimal determine the optimal solution to the dual problem, and if the solution is not optimal determine the new set of basic variables, the η matrix and use it to extend the B −1 to the new B −1 . Repeat this step (d) until the optimal solution is found. Page 2 of 3 APM236 HW5 due Wed. March 16 NAME: e) When optimal solution is found (in part (d), determine by how much we can change the resource 3 without changing the optimality/feasibility of the solution. f) If we change the value of b1 by +2 determine if the optimal solution would still be feasible, and if not try to x the problem by applying the dual simplex method. Page 3 of 3 ...
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