Practice Midterm 01

# Practice Midterm 01 - IEOR E4007 G. Iyengar March 10th,...

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IEOR E4007 G. Iyengar March 10th, 2009. IEOR E4007 Practice Midterm Instructions : 200pts 1. Simple problem on LP geometry 50pts The feasible region of the LP max x 1 +2 x 2 , s. t. 2 x 1 +3 x 2 20 , 3 x 1 x 2 20 , 0 x 1 6 , 0 x 2 6 . is shown below. x 1 x 2 x 3 x 4 x 5 (a) Compute the optimal solution of this LP. Is the optimal solution unique ? What is the optimal value ? 10pts (b) Suppose now the objective vector c θ = ± 1 2 ² + θ ± 2 1 ² Compute the range of θ for which the solution computed in part (a) remains optimal. 15pts 1

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(c) The objective vector in the above LP is c =(1 , 2) T . Construct a new objective vector c for which the points (4 , 4) T and (1 , 6) T are both optimal. 10pts (d) Construct a piecewise linear objective function for which the points (1 , 6) T ,(4 , 4) T and (6 , 1) T are all optimal. 15pts 2. Problem on sensitivity analysis 65pts A pottery manufacturer can make four kinds of dinner sets: English, Currier, Primrose, and Bluetail. Each set uses clay, enamel, dry room time, and kiln time; and results in a proFt shown in Table 1. Primrose can be made by two di±erent methods labeled P1 and P2 in Table 1. Currently the manufacturer is committed to producing the same
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## This note was uploaded on 06/02/2010 for the course IEOR IEOR E4007 taught by Professor Optimizationmodelsandmethods during the Summer '09 term at Columbia.

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Practice Midterm 01 - IEOR E4007 G. Iyengar March 10th,...

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