inequality problem: Minimize P = 500x + 350y subject to....

[Goods]

I am working on a problem and the answer seems way to obvious, which makes me nervous.

The problem is:

Minimize P = 500x + 350y subject to:

3x + 2y > 24
x + 2y > 16
x + y > 9
x > 0
y > 0

When I graphed this I got a region that looked like a pentagon w/verticies at: (0, 0) (8, 0) (6, 3) (2, 7) (0, 8).

Which would make the minimum point zero.

Can anyone see a mistake I may have made.

Thank you!

 

[tkhunny]

You are not looking at the right region.

You want to look at the region on the other side of your constraints. This gives you a whole new set of vertices to examine. (16,0), (0,12), (4,6).

One probably should point out that x + y >= 9 appears to be redundant.

 

[galactus]

I got x=4 and y=6, P=4100