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# OPTIMIZATION MATH 0164

UCLA

GPA 3.55

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This 2 page Class Notes was uploaded by Kaylin Wehner on Friday September 4, 2015. The Class Notes belongs to MATH 0164 at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 87 views. For similar materials see /class/177812/math-0164-university-of-california-los-angeles in Mathematics (M) at University of California - Los Angeles.

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Date Created: 09/04/15

Determine the optimal basic feasible solution of the linear program minimize 2 311 7 212 7 413 subject to 411 512 7 213 S 22 11 7 212 13 S 30 1112133132 S 0 Standard form of the problem H to CA3 5 533 minimize 2 subject to 411 512 7 213 31 311 7 212 7 413 22 30 11712713781782 S 0 112I21382 i Let 1 8182 1N 1112 13 we have a basic feasible solution 1 0002230Tl Check if 1 is optimal since 2 311 7 212 7 413 decreases if either 12 or 13 is increased from 0 Increase 13 from 0 and x 11 12 0 using 227411751221322213 3071121271330713 1 2 81 82 we observe that 13 can be increased until 13 30 When 13 30 32 0 thus we have 13 1331 1N 111282 and the basic feasible solution 1 0 0 30 82 0Tl Check if 1 is optimal Rewrite the 2nd constraints 2 in terms of 1N 11712 82 then we ave 31 227411 51223011212782 82761171272423 30711212782 4 and moreover 2 311 7 212 7 413 311 7 212 7 430 7 11 212 7 32 7120 711 71012 432 in terms of 1N 111282 Since this new objective function 2 decreases if 12 is increased from 0 Thus 1 is not optimal 3 Increase 12 from 0 and x 11 32 0 from the constraints 3 and 4 we have 31 82 7 12 and 13 30 212 Thus 12 can be increased until 12 82 When 12 82 31 0 thus we have 13 1312 1N 113132 and the basic feasible solution 1 0 82 30 2 96 82 0 0Tl Math 164 Handout Used for 521 General Formulae for the Simplex Method Andrea Brose May 19 2005 Consider the linear programming problem in standard form T minimize z c z subject to Ax b z 2 O with b 2 O 1 REORDERING Write l then T 2 c x 7 T T 3 7 CB 0N LN chB cExN 1 We then can rewrite problem as follows minimize z chB cExN 2 subject to En NzN b 3 20 B is basis matrix7 hence non singular7 ie B l exists 1see section 43 for notation

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