Question

8. (a) Write the dual of the following LPP: (5)

Minimize 16 1 9 2 21 3 Z = x + x + x

Subject to the constraints

x1 + x2 + x3 = 16

2x1 + x2 + x3 ≥12

x1

, x2 ≥ 0

3

x -unrestricted.

Answer 1

Max $z=7x_1+12x_2+4x_3$

   subject to-

       $x_1+x_2+x_3=16\\ 2x_1+x_2+x_3\ge 12\\ x_1,x_2,x_3\ge 0$

Dual is-

     Objective function- min  $10y_1+8y_2$

   constraints would be-

   $y_1+2y_1\ge 7\\2y_1-y_2\ge 12\\y_1+3y_2\ge 4\\ y_1,y_2\ge 0$

This is the dual of the Primal Problem.