SOLUTION: Maximize P=-21x+11y for the constraints x is greater than or equal to zero y is greater than or equal to zero y is greater than or equal to 4x-4 y is less than or equal to x

Algebra ->  College  -> Linear Algebra -> SOLUTION: Maximize P=-21x+11y for the constraints x is greater than or equal to zero y is greater than or equal to zero y is greater than or equal to 4x-4 y is less than or equal to x      Log On


   

Question 366386: Maximize P=-21x+11y for the constraints
x is greater than or equal to zero
y is greater than or equal to zero
y is greater than or equal to 4x-4
y is less than or equal to x+5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Plot Any Inequality
Graphing function x%3E=0:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%3E=0+%29


Solved by pluggable solver: Plot Any Inequality
Graphing function y%3E=0:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3E=0+%29



Solved by pluggable solver: Plot Any Inequality
Graphing function y%3E=4x-4:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3E=4x-4+%29



Solved by pluggable solver: Plot Any Inequality
Graphing function y%3C=x%2B5:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=x%2B5+%29


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Find the intersection of the bounding lines and the axes.
4x-4=0
x=1
(1,0)
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x=0
y=5
(0,5)
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4x-4=x%2B5
3x=9
x=3
y=x%2B5=8
(3,8)
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The minimum and maximum of your function occurs at one of the vertices.
(0,0):P=-21x%2B11y+=-21%280%29%2B11%280%29=0
(0,5):P=-21x%2B11y+=-21%280%29%2B11%285%29=highlight%2855%29
(1,0):P=-21x%2B11y+=-21%281%29%2B11%280%29=-21
(3,8):P=-21x%2B11y+=-21%283%29%2B11%288%29=-63%2B88=25