Interactive Linear Programming |
Min cX | |
Subject to: | |
and X0 | |
with c = |
So, we must: | |
Consider a new (m+1)*1 column-vector X= |
So, A was equal to: | |
and we add the new column, so that A becomes: |
So, vector C was equal to: | |
and we add | c_{n+1}=0 |
So that C becomes : | ( c_{1} | c_{2} | ... | c_{n} | 0 ) |
So, we must: | |
Consider a new (m+1)*1 column-vector X= |
So, A was equal to: | |
and we add the new column, so that A becomes: |
So, vector C was equal to: | |
and we add | c_{n+1}=0 |
So that C becomes : | ( c_{1} | c_{2} | ... | c_{n} | 0 ) |
The new variable (n+1)*1 column-vector is: |
So A, that was equal to | |
and becomes: |
a_{i,j}x'_{i}+a'_{i,j}x''_{i} |
=a_{i,j}(x'_{i}-x''_{i}) |
=a_{i,j}x_{i} |
c_{i}x'_{i}+c'_{i}x''_{i} |
=c_{i}(x'_{i}-x''_{i}) |
= c_{i}x_{i} |
The new vector C is the following: |
Maximize c_{1}x_{1} + c_{2}x_{2} +.....+ c_{n}x_{n} (Objective function) |
Minimize -c_{1}x_{1} - c_{2}x_{2} -.....- c_{n}x_{n} |