# Find an optimal solution for a system with matrix

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Imane hammou ouali on 7 Dec 2019
Edited: Matt J on 9 Dec 2019
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 on 7 Dec 2019
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.
Imane hammou ouali on 7 Dec 2019
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 on 9 Dec 2019
Note that x(1,2) has coefficient 0 in both the objective and constraints. It may as well not participate in the problem.

Matt J on 8 Dec 2019
f=-A(:);
Aineq=[B(:),C(:)].';
bineq=[4;3]
Xoptimal=linprog(f,Aineq,bineq)

Imane hammou ouali on 8 Dec 2019
Thank your for answering.But this is the result generated in matlab :
Xoptimal =
[]
Matt J on 9 Dec 2019
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.