how can i solve this with linprog command?

Hey there, need some help with the linprog command. im trying to solve this

 max =(7x1+7x2+6x3+9x4)

4x1+5x2+3x3+3x4<=30000
2x1+1.5x2+3x3+3x4<=22000 
x1,x2,x3,x4<=0

i tried this:

f = [7 7 6 9];
A = [4 5 3 3;2 1.5 3 3];
b = [30000 22000];
lb = [0 0 0 0];
x = linprog(f,A,b,[],[],lb)

Answer 1

[John D'Errico]

I'm confused. If you want to see:

x1,x2,x3,x4<=0

then why in the name of god and little green apples would you set a LOWER bound of all zeros?

lb = [0 0 0 0];

To me, this seems like a problem for an UPPER bound, not a lower bound.

Yes, I know that you are thinking you want to maximize. That is NOT the way to do it.

Instead, you need to negate the objective function.

f = -[7 7 6 9];
A = [4 5 3 3;2 1.5 3 3];
b = [30000;22000];
lb = [];
ub = [0 0 0 0]
x = linprog(f,A,b,[],[],lb,ub)

Optimization terminated.
x =
  -4.5475e-13
            0
            0
            0

It should be no surprise at all that the solution which MAXIMIZES f'*x for non-positive x is essentially x=zeros(4,1).

[Alvaro Vuyk]

wow, my bad x1,x2,x3,x4>=0

[John D'Errico]

So then what is the problem?

f = -[7 7 6 9];
lb = [0 0 0 0];

x = linprog(f,A,b,[],[],lb,[])
Optimization terminated.
x =
   2.4596e-06
       2285.7
   7.0595e-06
       6190.5

You maximize using a minimization tool by negating the objective.