Adding a constraint to "linprog" matlab example

HI, I'm working on the following example from matlab:

http://www.mathworks.com/help/optim/ug/linprog.html

Find x that minimizes

 f(x) = –5x1 – 4x2 –6x3,

subject to

x1 – x2 + x3 ≤ 20

3x1 + 2x2 + 4x3 ≤ 42

3x1 + 2x2 ≤ 30
0 ≤ x1, 0 ≤ x2, 0 ≤ x3.

First, enter the coefficients

f = [-5; -4; -6];

A =  [1 -1  1

        3  2  4

        3  2  0];

b = [20; 42; 30];

lb = zeros(3,1);

Next, call a linear programming routine.

 [x,fval,exitflag,output,lambda] = linprog(f,A,b,[],[],lb);

Here's my question: Iwould like to ad a new constraint:

x1= a+ b

x2= c+ d

x3= c+ e

The new constraint would be

14 ≤ a, 14 ≤ b, 14 ≤ c, 14 ≤ d

This mean that the previous answer:

x = 
     0.0000

      15.0000

       3.0000

Would not be ok since C=18 which is >14 in that case(meaning that linproog need to take into account the sum of A,B,C,D when he propose a solution for X)

Any Idea?

Thank you

Answer 1

[Matt J]

It's just a linear change of variables. If you make the substitutions

    x1= a+ b
    x2= c+ d
    x3= c+ e

in your original constraint inequalities (and objective function), you will get a new linear program in terms of a new unknown vector [a,b,c,d,e]. You can also add any further constraints on [a,b,c,d,e]that you like.

[Gimpy]

sorry it's not clear. The answer I'm looking for is the xi but I want it to satisfy my new condition. In that case I don't know how to specify my new constraint.

[Matt J]

Once you've transformed the linear program as I described above and solved for a,b,c,d,e you can recover the corresponding xi using the transformation equations,

    x1= a+ b
    x2= c+ d
    x3= c+ e