SOLUTION: Maximize z=4x+2y subject to x-y less than or equal to 10, 5x+3y less than or equal to 75, x+y less than or equal to 20, x greater than or equal to 0, y greater than or equal to 0

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Maximize z=4x+2y subject to x-y less than or equal to 10, 5x+3y less than or equal to 75, x+y less than or equal to 20, x greater than or equal to 0, y greater than or equal to 0      Log On


   

Question 881652: Maximize z=4x+2y subject to x-y less than or equal to 10, 5x+3y less than or equal to 75, x+y less than or equal to 20, x greater than or equal to 0, y greater than or equal to 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graph the constraints and find the vertex points.
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x-y=10
drawing%28300%2C300%2C-2%2C18%2C-2%2C18%2Cgraph%28300%2C300%2C-2%2C18%2C-2%2C18%2Cx-10%29%29
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5x%2B3y=75

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x%2By=20

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Find the points of intersection.
x-y=10
x%2By=20
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2x=30
x=15
15%2By=20
y=5
(15,5)
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x-y=10
5x%2B3y=75
5x-5y=50
8y=25
y=25%2F8
x-25%2F8=80%2F8
y=105%2F8
(25/8,105/8)
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x%2By=20
5x%2B3y=75
5x%2B5y=100
2y=25
y=25%2F2
x%2B25%2F2=40%2F2
x=15%2F2
(15/2,25/2)
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The extrema of the function occurs at these points.
z=4x%2B2y=4%2815%29%2B2%285%29=60%2B10=70
z=4x%2B2y=4%28105%2F8%29%2B2%2825%2F8%29=420%2F8%2B50%2F8=470%2F8=235%2F4
z=4x%2B2y=4%2815%2F2%29%2B2%2825%2F2%29=30%2B25=55
The maximum values is z=70