IE220_F08_hw1sol

IE220_F08_hw1sol - IE220: Introduction to Operations...

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Unformatted text preview: IE220: Introduction to Operations Research Fall 2008 Prof. Imre Polik Homework 1 Solutions 3.1-8 Let x 1 denote the number of units of special risk insurance and x 2 the number of units for mortgages. The optimization problem is max 5 x 1 + 2 x 2 3 x 1 + 2 x 2 2400 x 2 800 2 x 1 1200 x 1 ,x 2 The feasible set is shown in the following figure: 200 400 600 800 200 400 600 800 1000 1200 x 1 x 2 3 x 1 + 2 x 2 2400 2 x 1 1200 x 2 800 max5 x 1 + 2 x 2 (600 , 300) After graphing the constraints the optimal solution turns out to be at the intersection of the constraints 2 x 1 = 1200 and 3 x 1 + 2 x 2 = 2400, which implies x 1 = 600, x 2 = 300. The optimal objective function value is Z = 3600. 1 3.1-12 The point (2 , 3) satisfies the constraint kx 1 + x 2 2 k +3 with equality for all values of k , thus this constraint boundary always passes through the point. The other end of this constraint x 1 x 2 1 2 3 4 5 6 7 8 1 2 3 4 5 x 2 3- x 1 + x 2 2 kx 1 + x 2 2 k + 3 max x 1 + 2 x 2 ( 2 + 3 k , ) boundary (see the figure) is on the...
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This note was uploaded on 09/24/2008 for the course IE 220 taught by Professor Storer during the Fall '07 term at Lehigh University .

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IE220_F08_hw1sol - IE220: Introduction to Operations...

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