Solve the following by applying the simplex algorithm to the

Solve the following by applying the simplex algorithm to the dual. Minimize 8.x1 + I3x2 + 20x3 subject to

Solution

Given: minimize:8x1+13x2+20x3 ---------------(1)

                 subject to:3x1+2x2+x3>=2 ---------------(2)

                                   x1-x2+2x3>=4 ---------------(3)

                                  2x2+2x3>-1 ---------------(4)

                                  -2x1+3x3>=0 ---------------(5)

                                  4x1-x3>=-2 ---------------(6)

    if solve (5) and (6) then got 3x1+2x3=-2

                                                 3x1=-2+2x3 ------------(7)

             and from (2) 2x2=-1-2x3 ------------(8)

(7),(8) subtude in (2)

   then x3=5 then from(7) x1=8/3

               and from (3) and x3,x1 then x2=26/3

so we know all x1,x2,x3 values so substute in (1)                               

    then minimize is:8(8/3)+13(26/3)+20(5)

                           =712/3

                         =227.33