Linear Optimization: Mixed Constraint Equation Question

Question

Brian 2012-9-23

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Hello, all, thanks for reading this.

I have a question about a simple linear optimization problem. I am running a example I found online, so I can compare this to GAMS, and I am unsure on how to use these constraint equations:

 % Governing Equation
% Maximize Z = x1+5x2
% 
% Constraint Equations:
% x1 + 3x2 <= 5;
% 2x1 + x2 = 4;
% x1 - 2x2 >= 1;
% x1,x2 >= 0;

I know from earleir examples I would use the code:

 f = [-1; -5;]; % negative b/c linprog minimization
A = [1 3;
    ? ?;
    -1 2];
b = [5; ?; -1];
 options = optimset('LargeScale', 'off');
xsol = linprog(f,A,b,[],[],[],[],[],options)

However, since I have one equality constraint, I have 1 DOF and I am not sure how to translate this to MATLAB. Would I leave the equality constraint out of the equation and linprog?

Thanks for your advice. I am unsure how to apply equality constraints in this type of problem.

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Answer 1

Rodrigo 2012-9-24

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This can be done by hand, but assuming this is a template for a more complicated problem, you would need to use Aeq and beq to handle the equalities. The last pair of conditions require lb and ub.

f = [-1; -5;]; % negative b/c linprog minimization A = [1, 3;-1, 2]; b = [5; -1]; Aeq=[2,1]; beq=4; lb=[0;0]; ub=[Inf;Inf]; xsol = linprog(f,A,b,Aeq,beq,lb,ub);

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Brian 2012-9-26

Yes, thank you for your help! I checked some more documentation online, and I had problems with understanding the linprog function itself. I should have looked online more before I posted.

Thanks for your help!

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