p1 - OR&IE 320/520 Summer 2006 Prelim #1 May...

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Unformatted text preview: OR&IE 320/520 Summer 2006 Prelim #1 May 31, 2006 Closed book. Justify all work. 1. In class we solved the following LP problem using the simplex algorithm: ORIGINAL PROBLEM max 4 x 1 + 3 x 2 s.t. 3 x 1 + x 2 9 3 x 1 + 2 x 2 10 x 1 + x 2 4 x 1 , x 2 FINAL REPRESENTATION max 14- x 4- x 5 s.t. x 4- 2 x 5 + x 1 = 2- x 4 + 3 x 5 + x 2 = 2- 2 x 4 + 3 x 5 + x 3 = 1 x 4 , x 5 , x 1 , x 2 , x 3 . (a) (4 points) Explain why the variables x 3 , x 4 , x 5 appear in the final, but not in the original problem representation. (b) (4 points) What is the basic solution specified by the final representation? Indicate which variables are basic and which are nonbasic. (c) (6 points) What is the basis matrix, i.e., matrix B , for the final solution. (d) (6 points) Determine B- 1 from this data by inspection. (e) (8 points) Give the algebraic expression for the updated right-hand side vector, b , using B- 1 and the original problem data. If the original right-hand side vector (9 ,...
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p1 - OR&IE 320/520 Summer 2006 Prelim #1 May...

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