Question

Write down the associated dual problem.

(ii)Given the information that the optimal basic variables are 1xand 3x, determine the associated optimal dual solution (1y, 2y and w).

Maximize subject to z = x, +5x2 + 3x3 x, + x2 + x3 = 3 2x, - x2 = 4 *,,X, X, 20 (i) Write down the associated dual problem. (5 marks) (ii) Given the information that the optimal basic variables are x, and xz, determine the associated optimal dual solution (y,, y, and w). (5 marks)

Answer 1

2 - Giren primal problem es maximize Z = X 757, f 3x ! subject to a tre ti=3 2x x2 = 4 sy, 592 - 6 34,32,350 ☺ The w associated Y. and Y Dual problem ein es geven as . the variable minimize zw=3y +44 subject to 9, +242:21 Yy-zy, as y, > 3 — 121 where I, I, es unrestricted en sean ii to fend solution lution of of w W we have to we have equations (2 by using solve graphical method

9, +2y, = 1. when y. -24, -5 then go = y, s and = 3. Now we draw the - xen region 92 (1.) (0,0.5) 2 4 sls, oh whts 3, +24, 1 9,-24, Es Thus the shaded region is optimal region in which only one comer poent A(8,0).

Theis the value of w = 34, + 4y at point (5.0). =3*5 +4xo Eis. This [w=is at (I1, I₂ ) = (5.0) Theis is the optimal 15. at the soluation of dual problem basic variable G 9 ) =15, oj so the optimal Pretnal problem has ako the solution. score Izzis