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4. Primal to dual conversion example ( Enter your problem )
  1. Rules & Example-1
  2. Example-2
Other related methods
  1. Simplex (BigM) method
  2. Two-Phase method
  3. Graphical method
  4. Primal to dual conversion
  5. Dual simplex method
  6. Integer simplex method
  7. Branch and Bound method
  8. 0-1 Integer programming problem

2. Example-2


Find dual from primal conversion
MIN z = x1 - 3x2 - 2x3
subject to
3x1 - x2 + 2x3 <= 7
2x1 - 4x2 >= 12
-4x1 + 3x2 + 8x3 = 10
and x1,x2 >= 0 and x3 unrestricted in sign


Solution:
Primal is (Solution stpes of Primal by BigM method)

MIN `z_x``=``````x_1`` - ``3``x_2`` - ``2``x_3`
subject to
```3``x_1`` - ````x_2`` + ``2``x_3``7`
```2``x_1`` - ``4``x_2``12`
` - ``4``x_1`` + ``3``x_2`` + ``8``x_3`=`10`
and `x_1,x_2 >= 0; ``x_3` unrestricted in sign


all `<=` constraints can be converted to `>=` type by multipling both sides by -1

MIN `z_x``=``````x_1`` - ``3``x_2`` - ``2``x_3`
subject to
` - ``3``x_1`` + ````x_2`` - ``2``x_3``-7`
```2``x_1`` - ``4``x_2``12`
` - ``4``x_1`` + ``3``x_2`` + ``8``x_3`=`10`
and `x_1,x_2 >= 0; ``x_3` unrestricted in sign


The `x_3` variable in the primal is unrestricted in sign, therefore the `3^(rd)` constraint in the dual shall be equality.

Since `3^(rd)` constraint in the primal is equality, the corresponding dual variable `y_3` will be unrestricted in sign.

Dual is (Solution stpes of Dual by BigM method)

MAX `z_y``=`` - ``7``y_1`` + ``12``y_2`` + ``10``y_3`
subject to
` - ``3``y_1`` + ``2``y_2`` - ``4``y_3``1`
`````y_1`` - ``4``y_2`` + ``3``y_3``-3`
` - ``2``y_1`` + ``8``y_3`=`-2`
and `y_1,y_2 >= 0; ``y_3` unrestricted in sign





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