Posted by **Chelsea** on Thursday, August 25, 2011 at 1:35pm.

Maximize z=4x+2y subject to:

x-y<10

5x+3y<75

x+y<20

X>0

y>0

- Algebra -
**Reiny**, Thursday, August 25, 2011 at 1:59pm
make a sketch and shade in the region.

(I used the intercepts of the corresponding equations to draw the lines)

I got a region with critical points of (13.125, 3.125) and (7.5, 12.5) inside the first quadrant after solving the simple equations.

Slide the line 4x + 2y = z parallel to itself until you reach the farthest point of the region.

I found that to be (13.125, 3.125)

so z = 4(13.125) + 2(3.125) = 58.75

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