maximization problem , linprog optimization

Hello,

I'm trying to solve this maximization problem with matlab.

Answer 1

[Sulaymon Eshkabilov]

Here is a nice documentation showing several examples how to apply linprog() fcn of MATLAB to solve such exercises:

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

[Matt J]

Also, you could use a problem-based workflow,

https://www.mathworks.com/help/optim/ug/problem-based-workflow.html

[xu]

I tried this one and it was not optimised well.

A=[0 -0.0123 0.738;0.0069 0.0069 0.828];
b=[-0.123;2.001];
lb=[160;10;0];
ub=[220;70; ];
f=[0;0;-1];
Aeq = [];
beq = [];
[x,favl]=linprog(f,A,b,Aeq,beq,lb,ub);

Warning: Length of upper bounds is < length(x); filling in missing upper bounds with +Inf.

Optimal solution found.

f1=0*x(1)+0.0123*x(2);
f2=-0.0069*x(1)-0.0069*x(2);

[Matt J]

Why do you think anything is wrong, apart from the warning?

[xu]

Since the optimal solution obtained from the literature was rather different from the one I got, I wondered if there was something wrong with my code.

[Matt J]

You should have,

ub=[220;70; +inf];

but that won't make a difference to the result.

[Matt J]

You can double check things with the problem-based approach:

lam=optimvar('lambda',1,'Lower',0);
x=optimvar('x',[2,1],'Lower',[160,10],'Upper',[220,70]);

Con.Con1=0.0123*x(2)-0.738*lam>=0.123;
Con.Con2=-0.0069*sum(x)-0.828*lam>=-2.001;

prob=optimproblem('Objective',lam,'ObjectiveSense','max','Constraints',Con);

sol=solve(prob)

Solving problem using linprog.

Optimal solution found.

sol = struct with fields:
    lambda: 0.6667
         x: [2×1 double]