IE513_hw2-1 - Max 2 1 3 2 x x + s.t. 9 6 4 2 2 1 2 1 2 1...

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IE 513 Linear Programming Spring 2009-2010 Homework 2 Due February 12, 2010 Q 1.25 : Consider the following linear programming problem. Min 3 2 1 3 2 x x x - - s.t. 3 2 12 4 2 14 2 3 3 2 1 3 2 1 3 2 1 - = + - + + + + x x x x x x x x x x a) Reformulate the problem so that it is in standard format. b) Reformulate the problem so that it is in canonical format. c) Convert the problem into a maximization problem. Q 1.27 : Consider the following problem. Max 2 1 x x - s.t. 0 0 3 3 0 2 2 1 2 1 2 1 - + - + - x x x x x x a) Sketch the feasible region in the ) , ( 2 1 x x space. b) Identify the region in the ) , ( 2 1 x x space where the slack variables 3 x and 4 x , say, are equal to zero. c) Solve the problem geometrically. d) Draw the requirement space and interpret feasibility. 1

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Q 1.2 9 : Consider the following problem.
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Unformatted text preview: Max 2 1 3 2 x x + s.t. 9 6 4 2 2 1 2 1 2 1 ≥ ≥ ≤ + ≤ + x x x x x x a) Sketch the feasible region. b) Find two alternative optimal extreme (corner) points. c) Find an infinite class of optimal solutions. Q 1.32 : Consider the following problem: Minimize cx subject to b Ax ≥ , ≥ x . Suppose that one component of the vector b , say b i , is increased by one unit to b i + 1. a) What happens to the feasible region? b) What happens to the optimal objective? Q 1.33 : From the results of the previous problem, assuming i b z ∂ ∂ / * , exists, is it ≤ , = 0, or ≥ ? 2...
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This note was uploaded on 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.

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IE513_hw2-1 - Max 2 1 3 2 x x + s.t. 9 6 4 2 2 1 2 1 2 1...

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