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assignment8_ProblemSet - maximize x(P x = 1 x ≥ with a...

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ORIE 3300/5300 ASSIGNMENT 8 Fall 2008 *NOT TO BE TURNED IN** Individual work. Solutions will be posted 5 pm, Friday November 7. 1. Consider the linear programming problem max 3 x 1 + 2 x 2 + 3 x 3 2 x 1 + x 2 + x 3 3 3 x 1 + x 2 + 2 x 2 5 x 1 , x 2 , x 3 0 . Add slack variables and solve this problem by the revised simplex method, starting with the all-slack basis. 2. This question is concerned with the linear programming problem in Q2 of Assignment 7. (a) Write out the dual of this problem. (b) Use your answer for Q2 last week to find the optimal solution of the dual problem you found in (a). (c) Give a short certificate that the solution you found in (b) is indeed the optimal solution of the dual problem. 3. Consider the linear program
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Unformatted text preview: maximize x (P) x = 1 x ≥ , with a single constraint on a single variable x . (a) What is the dual problem (D)? (b) For each of (P) and (D), state whether it is infeasible, unbounded, or has an optimal solution. (c) Now suppose the “0” in the constraint is replaced by a small number ± > 0. How does your answer in (b) change? What if it is replaced by-± ? If you call the optimal value of an infeasible maximization prob-lem-∞ and that of an unbounded maximization problem + ∞ , how does the optimal value of (P) vary as a function of a , the coefficient of x in the constraint? 1...
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