Problem is unbounded in linear programming

I have this solution for a linear programming . I have used the linprog function , but I get showed the answer : Problem is unbounded .

Please if you can help me how to fix this problem .

The code is below :

AT = [1 4 2 3;

4 5 3 1];

u = [300 400];

g = [320 510 430 300];

z = linprog(g,AT,u);

[Chendi Lin]

Hi Klaus,

Is there any missing lower bound or upper bound for the design variables?

For example, if all your design variables are non-negative, then you will have

lb = zeros(4,1);
ub = [];
z = linprog(g, AT, u, [], [], lb, ub);

Please refer to this document to see the syntax for linprog: Solve linear programming problems - MATLAB linprog (mathworks.com).

Thanks,

CD

[Klaus Hajdaraj]

Thank your for your answer !

Yes , I expect only positive values , but when I try the code with ub and lb like you suggested me , the result is 0 0 0 0.

I expect a different result , postitive non zero numbers.

Answer 1

[Chendi Lin]

Hi Klaus,

Because all your design variables are non-negative, you will have

AT = [1 4 2 3;
      4 5 3 1];
u = [300 400];
g = [320 510 430 300];
lb = zeros(4,1);
ub = [];
z = linprog(g, AT, u, [], [], lb, ub);

Notice that, linprog solves a minimization problem. Intuitively, the result is a zero vector. To make it a maximization problem, you can use

z = linprog(-1*g, AT, u, [], [], lb, ub);

And the result is [0; 0; 128.57; 14.29] now.

Please refer to this document to see the syntax for linprog: Solve linear programming problems - MATLAB linprog (mathworks.com).

Thanks,

CD

[Klaus Hajdaraj]

Thank you a lot !