SOLUTION: PLEASE HELP !! Maximize: z=3x+5y given the constraints 4x+7y <= 28 10x - 7y <=28 x >= 0 y >= 0

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Question 966510: PLEASE HELP !!
Maximize:
z=3x+5y given the constraints
4x+7y <= 28
10x - 7y <=28
x >= 0
y >= 0

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First map the feasible region.
.
Find the point of intersection.
4x%2B7y=28
10x-7y=28
Add the equations together,
14x=56
x=4
Then,
16%2B7y=28
7y=12
y=12%2F7
Now from the graph, you have all the vertices of the feasible region.
(0,0)
(0,4)
(14%2F5,0)
(4,12%2F7)
The extrema of the function occur at these vertices.
(0,0) : z=3%280%29%2B5%280%29=0
(0,4): z=3%280%29%2B5%284%29=20
(14%2F5,0): z=3%2814%2F5%29%2B5%280%29=42%2F5=8.4
(4,12%2F7): z=3%284%29%2B5%2812%2F7%29=12%2B60%2F7=84%2F7%2B60%2F7=144%2F7=20%264%2F7