Minimize 2 x 1 + 3 x 2 + 3 x 3 + 6 x 4 + 4 x 5 Subject to 2 x 1 + x 2 − 2 x 3 + 3 x 4 − 2 x 5 = − 1 x 1 + 3 x 2 + x 3 + 2 x 4 + x 5 = 1 x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 , x 4 ≥ 0 , x 5 ≥ 0.

Question

Minimize   2      x    1    +  3      x    2    +  3      x    3    +  6      x    4    +  4      x    5  Subject to  2      x    1    +      x    2    −  2      x    3    +  3      x    4    −  2      x    5    =  −  1      x    1    +  3      x    2    +      x    3    +  2      x    4    +      x    5    =  1      x    1    ≥  0  ,      x    2    ≥  0  ,      x    3    ≥  0  ,      x    4    ≥  0  ,      x    5    ≥  0.

Raven Hawkins · Accepted Answer

The dual problem is:objective function  max     −      y    1    +      y    2  constraints  2      y    1    +      y    2    ≤  2      y    1    +  3      y    2    ≤  3  −  2      y    1    +      y    2    ≤  3  3      y    1    +  2      y    2    ≤  6  −  2      y    1    +      y    2    ≤  4      y    1    ,      y    2   are unrestricted.You have to solve every constraint for       y    2  . Then you can draw the constraints in a       y    1    −      y    2  -coordinate system. If you consider the inequality-signs you will get a solution space.Now you set the objective function equal to zero and solve the equation for       y    2  . After you have drawn it in the coordinate system you have to move it parallel till you just touch the solution space.

Minimize 2x_1+3x_2+3x_3+6x_4+4x_5 Subject to 2x_1+x_2−2x_3+3x_4−2x_5=−1, x_1+3x_2+x_3+2x_4+x_5=1, x_1≥0,x_2≥0,x_3≥0,x_4≥0,x_5≥0.

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