We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more   

AtoZmath.com
Support us
(New) All problem can be solved using search box
I want to sell my website www.AtoZmath.com with complete code
Home What's new College Algebra Games Feedback About us
Algebra Matrix & Vector Numerical Methods Statistical Methods Operation Research Word Problems Calculus Geometry Pre-Algebra


Home > Operation Research calculators > Primal to dual conversion example
4. Primal to dual conversion example ( Enter your problem )
( Enter your problem )
  1. Formulation and Rules
  2. Example-1
  3. Example-2
  4. Example-3
  5. Example-4
  6. Example-5
  7. Example-6
 		Other related methods
  1. Formulate linear programming model
  2. Graphical method
  3. Simplex method (BigM method)
  4. Two-Phase method
  5. Primal to dual conversion
  6. Dual simplex method
  7. Integer simplex method
  8. Branch and Bound method
  9. 0-1 Integer programming problem
  10. Revised Simplex method
6. Example-5
(Previous example)		6. Dual simplex method
(Next method)

7. Example-6


Find dual from primal conversion
MAX z = x1 - 2x2 + 3x3
subject to
-2x1 + x2 + 3x3 = 2
2x1 + 3x2 + 4x3 = 1
and x1,x2,x3 >= 0

Solution:
Primal is (Solution steps of Primal by Simplex method)

MAX `z_x``=``````x_1`` - ``2``x_2`` + ``3``x_3`
subject to
` - ``2``x_1`` + ````x_2`` + ``3``x_3`=`2`
```2``x_1`` + ``3``x_2`` + ``4``x_3`=`1`
and `x_1,x_2,x_3 >= 0; `


In primal, There are `3` variables and `2` constraints, so in dual there must be `3` constraints and `2` variables

In primal, The coefficient of objective function `c_1=1,c_2=-2,c_3=3` becomes right hand side constants in dual

In primal, The right hand side constants `b_1=2,b_2=1` becomes coefficient of objective function in dual

In primal, objective function is maximizing, so in dual objective function must be minimizing

Let `y1,y2` be the dual variables

Since `1^(st),2^(nd)` constraints in the primal are equalities, the corresponding dual variables `y_1,y_2` will be unrestricted in sign.

Dual is (Solution steps of Dual by Simplex method)

MIN `z_y``=````2``y_1`` + ````y_2`
subject to
` - ``2``y_1`` + ``2``y_2`≥`1`
`````y_1`` + ``3``y_2`≥`-2`
```3``y_1`` + ``4``y_2`≥`3`
and ```y_1,y_2` unrestricted in sign


This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here


6. Example-5
(Previous example)		6. Dual simplex method
(Next method)


Share this solution or page with your friends.


Home What's new College Algebra Games Feedback About us
 
Copyright © 2024. All rights reserved. Terms, Privacy
 
 

.