Find an optimal solution for a system with matrix

Hello exper,

I have a marix A=[0.8 0 ; 1 0.8] that i should maximize its elements : Max sum(A)

I have like Contraints sum(B)<= 4 , and B is a matrix B=[1 0 ;2 2]

an other constraint sum(C)<=3 , and C is a matrix C=[1 0 ;1 1]

I will be very grateful if you can help me

[Image Analyst]

It's trivial:

A = [inf, inf; inf, inf]; % Maximize values of elements in A

Note that no relationship at all between A and either B and/or C was specified, so we can just ignore B and C.

Read this link

[Imane hammou ouali]

i want to maximize the sum of matrix A ,

its just like max ( 0.8x(1,1)+0 x(1,2)+ 1x(2,1)+0.8x(2,2) )

1x(1,1)+0 x(1,2)+ 2x(2,1)+2x(2,2) <=4

x(1,1)+0 x(1,2)+ 1x(2,1)+1x(2,2)<=3

[Matt J]

Note that x(1,2) has coefficient 0 in both the objective and constraints. It may as well not participate in the problem.

Answer 1

[Matt J]

f=-A(:);
Aineq=[B(:),C(:)].';
bineq=[4;3]


Xoptimal=linprog(f,Aineq,bineq)

[Imane hammou ouali]

Thank your for answering.But this is the result generated in matlab :

Xoptimal =

[]

any help please

[Matt J]

The problem is unbounded and has no finite solution. You need more constraints. If I assume all the X(i) are meant to be non-negative, then we get the following solution,

>> Xoptimal=linprog(f,Aineq,bineq,[],[],[0 0 0 0]);

>> reshape(Xoptimal,2,2)

ans =

    2.0000         0
    1.0000         0

Note that X(1,2) can really be chosen as any non-negative value since it does not contribute to the problem, as I mentioned above.