SOLUTION: Maximize: C = 3x + 4y Constraints: x + y ≤ 10 – x + y ≤ 5 2x + 4y ≤ 32

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Question 926184: Maximize:
C = 3x + 4y
Constraints:
x + y ≤ 10
– x + y ≤ 5
2x + 4y ≤ 32

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First, map out the feasible region.
x%2By%3C=10
y%3C=-x%2B10
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graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C-x%2B10%29
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graph%28300%2C300%2C-3%2C12%2C-3%2C12%2Cy%3C=-x%2B10%29
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-x+%2B+y+%3C=5
y%3C=x%2B5
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graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C-x%2B10%2Cx%2B5%29
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2x%2B4y%3C=32
x%2B2y%3C=16
2y%3C=-x%2B16
y%3C=-x%2F2%2B8
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graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C-x%2B10%2Cx%2B5%2C-x%2F2%2B8%29
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Find the vertices of the intersection points.
-x%2F2%2B8=x%2B5
-x%2B16=2x%2B10
3x=6
x=2
Then,
y=2%2B5
y=7
(2,7)
and
-x%2F2%2B8=-x%2B10
-x%2B16=-2x%2B20
x=4
Then,
y=-4%2B10
y=6
(4,6)
Also include,
(0,5) and (10,0).
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Now check the function using these points:
(2,7)
C+=+3x+%2B+4y=3%282%29%2B4%287%29=6%2B28=34
(4,6)
C+=+3x+%2B+4y=3%284%29%2B4%286%29=12%2B24=36
(0,5)
C+=+3x+%2B+4y=3%280%29%2B4%285%29=0%2B20=20
(10,0)
C+=+3x+%2B+4y=3%2810%29%2B4%280%29=30%2B0=30
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The maximum occurs at (2,7)