Minimize a function under several constraints

Hello community can anyone help me solve this problem please.

I have to minimize this:

F= P1*X1+P2*X2+P3*X3+P4*X4

s.t P1X1+P3X3 ≤ L1

P2X2+P4X4 ≤ L1

P1X1+P2X2=E1

P3X3+P4X4=E2

P1,P2,P3,P4,L1,L2,E1,E2 are known.

X1,X2,X3,X4 are the unknown variables, they must be binary .

Answer 1

[Matt J]

Use intlinprog() or,

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

[Imanitxka imane]

Implementation with intlinprog, please Matlab code

[Matt J]

In fact my program is very large, I reduce it just to find a simple solution

So you are just looking for simplified examples? If so, the Examples in the documentation should serve quite well,

https://www.mathworks.com/help/optim/ug/intlinprog.html#bts3f9f-4

Answer 2

[Steven Lord]

Any values that satisfy your first two constraints are a solution to the problem since your objective function is constant. Substitute the third and fourth constraints into the objective function to see that this is the case.

In this small case you don't need intlinprog. Brute force is sufficient.

[Imanitxka imane]

In fact my program is very large, I reduce it just to find a simple solution