Hw6_solution

# Hw6_solution - 1 Introduction to Mathematical Programming...

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1 Introduction to Mathematical Programming IEOR 3608 Prof. Maria Chudnovky Homework #6 Solution 1. Use the two-phase simplex method to find a BFS. ( You can use the big M method as well.) Firstly, transform the constraints into 1 2 3 1 1 1 2 3 1 1 2 3 2 2 2 2 3 10 5 x x x e a x x x s x x x a + − + = + + + = + + + = Phase I LP: 1 2 1 2 3 1 1 1 2 3 1 1 2 3 2 min ' . . 2 2 2 3 10 5 w a a s t x x x e a x x x s x x x a = + + − + = + + + = + + + = New row 0: 1 2 3 1 ' 2 2 7 w x x x e + + = ' w 1 x 2 x 3 x 1 s 1 e 1 a 2 a rhs BV Ratio 1 2 -1 2 0 -1 0 0 7 ' w 0 [1] -2 1 0 -1 1 0 2 1 a * 2 0 2 1 3 1 0 0 0 10 1 s 5 0 1 1 1 0 0 0 0 0 2 a 5 ' w 1 x 2 x 3 x 1 s 1 e 1 a 2 a rhs BV Ratio 1 0 3 0 0 1 -2 0 3 ' w 0 1 -2 1 0 -1 1 0 2 1 x None 0 0 5 1 1 2 -2 0 6 1 s 6 5 0 [3] 0 0 1 1 1 3 2 a * 1

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2 ' w 1 x 2 x 3 x 1 s 1 e 1 a 2 a rhs BV Ratio 1 0 0 0 0 0 -1 -1 0 ' w 0 1 0 1 0 1 3 1 3 2 3 4 1 x 0 0 0 1 1 1 3 1 3 5 3 1 1 s 0 0 1 0 0 1 3 1 3 1 3 1 2 x So a BFS is : 1 2 3 4, 1, 0 x x x = = = . Actually another two BFSs are :
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Hw6_solution - 1 Introduction to Mathematical Programming...

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