Question

10. What is the dual of the following problem: Minimize x1 + x2, subject to xi 20, x2 > 0, 2xı > 4, x1 + 3x2 > 11? Find the solution to both this problem and its dual, and verify that minimum equals maximum.

Answer 1

solution : Given problem is Min 2 = 24+22 subject to 224 7,4 24797,711 21,4,7, net , 2 br are the dual variables. so the dual problem is. Max W = 494 + 1172 subject to 24 ty El 37,41 2 2 710. now me to solve the above problem apply First me some the problem no 1. as follows Minzel utan Z 224 = 4 of 422 sy + 32 22 11 57 1 + g = 1

e! thos 2 R sine the optimal area is infinté me get the optinal point B(2,3). (by solving @50) Minz= 4+22 when 24-2, 12²3. 2+3 25 min 2-5 3 2 2 923, wow me solve the dual problen. (2) max 2 = 4 4 + 119 22 + y 2 21. 90 D2 = 1. B & 72 R 372 = 1 27 72 73 solving & D 244 + 1 - * !-Y = 73 7 = 43., & J 273

Fodbold + 1 k + 2 g o 5 A Be we get the optima arca. whese 0:(09) 4:(,0) * (Ys, '), e:(,'). now me compute sue optimal tarble (optimal point max word,+ 11Y, 0,0) 2 6,0) 5 1/2 .. clearly me see that Max wa 5) when. = 22, 223 / 3 min 22 Maxwas ie the minimumot 2 is equl to the maximum of its dual w. (verified). me see that