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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 method (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
  9. Revised Simplex method

1. Rules & Example-1



Rules
In Primal Then in Dual
1. Objective function is maximum Objective function is minimum
2. `x_1` unrestricted in sign `1^"st"` constraint is = type
3. `1^"st"` constraint is = type `y_1` unrestricted in sign
4. constraint is `<=` type constraint is `>=` type
5. Objective function : total 3 variables (`x_1,x_2,x_3`) and coefficient `c_1,c_2,c_3` constraints : total 3 constraints and right hand side constraint `b_1,b_2,b_3`.
(`c_1` becomes `b_1`, `c_2` becomes `b_2`, `c_3` becomes `b_3`)
6. constraints : total 2 constraints and right hand side constraint `b_1,b_2` Objective function : total 2 variables (`y_1,y_2`) and coefficient `c_1,c_2`.
(`b_1` becomes `c_1`, `b_2` becomes `c_2`)

Example-1
Find dual from primal conversion
MAX z = x1 - x2 + 3x3
subject to
x1 + x2 + x3 <= 10
2x1 - x2 - x3 <= 2
2x1 - 2x2 - 3x3 <= 6
and x1,x2,x3 >= 0


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

MAX `z_x``=``````x_1`` - ````x_2`` + ``3``x_3`
subject to
`````x_1`` + ````x_2`` + ````x_3``10`
```2``x_1`` - ````x_2`` - ````x_3``2`
```2``x_1`` - ``2``x_2`` - ``3``x_3``6`
and `x_1,x_2,x_3 >= 0; `


Dual is (Solution stpes of Dual by BigM method)

MIN `z_y``=````10``y_1`` + ``2``y_2`` + ``6``y_3`
subject to
`````y_1`` + ``2``y_2`` + ``2``y_3``1`
`````y_1`` - ````y_2`` - ``2``y_3``-1`
`````y_1`` - ````y_2`` - ``3``y_3``3`
and `y_1,y_2,y_3 >= 0; `





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