# smid - 1 Converi ihe foliowing iieear programming problem...

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Unformatted text preview: 1. Converi ihe foliowing iieear programming problem to standerd form and thee mite oat {he eeefﬁciegt matrix A Maximize 3:51 W 372 +4 subject to 5V W \$1” 332 H 0.: —2\$1 4“ 3352 \$1 S 21\$2f’r53 2. Lie solving a éieear programming problem by éhe simplex method, we arrive at the objective function in the form Z = M2\$3+3\$4+éi5+7 and the éictioaeﬁr 331 3 W333:§“3\$4+\$5+4 \$32m\$3+\$4+2\$5+1 Use the Simplex algorithm to ﬁnd the optimal soiuéion to the problem. 3. Consider the iinee: programﬁﬁng problem Minimize z. m 33;] w 3:2 + 1‘3 subject to \$1 “4” .752 ~’ Z 1 2x1 + \$3 2 4 “:32 + 933 2 0 \$171.23 173 R 0 {a} Show that a: x {2, 1, If is a feasibie solution to the proﬁlem. (b) Show that p 2 (8, “3, m2? is a feasible direciion at the feasible solution 3: r (27 1, 1)? (e) Deéermine éhe maximal step iength (X each that. :3 + Ox 3} remains fee— sible, where 3'; ami p is as in part {b}. (Ci) Finci the mieie’mm value ef :21, such teat p 2 {391, MB, WE)? is a feasibﬁe direetéee at :5 2 1, 1}? 4. Consiéex tee Linea; pmgzaxmnieg problem below. (21} Write the dual Eigear yregremming problem, (33) Given that (3/5, 8/510, 9)? is an optimal selutiee :30 the given minimizatiee prebéem, use compiementaxy slackness to solve the dual probiem. Minimize z : Winn —— 552 subject \$0 "2351 + 3552 + 233 M 6 3.3571 2552 + 33:; x 5; \$1,333 3331334 2 U 5. Given that the feasible set of a iieear programnﬁng prebiem is bounded, and. tiaerefore every feasibie peiet is a eem'ex combination of extreme point-s; prove Enha‘t if the problem has an optimal solution, then it has an optimal solution that is an exireme paint. [\3 ...
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## This note was uploaded on 01/18/2011 for the course MATH Math 164 taught by Professor Brown during the Spring '10 term at UCLA.

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smid - 1 Converi ihe foliowing iieear programming problem...

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