SOLUTION: Solve the equation: Z = 4x + y knowing that: x + 2y <= 40 x + y <= 30 2x + 3y <= 66 both x and y are >= 0

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Question 923166: Solve the equation:
Z = 4x + y
knowing that:
x + 2y <= 40
x + y <= 30
2x + 3y <= 66
both x and y are >= 0
Found 2 solutions by Fombitz, chawki:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B2y%3C=40
2y%3C=-x%2B40
y%3C=-x%2F2%2B20
Graph y=-x%2F2%2B20
graph%28300%2C300%2C-10%2C40%2C-10%2C40%2C-x%2F2%2B20%29
.
.
x%2By%3C=30
y%3C=-x%2B30
Graph y=-x%2B30 also.
graph%28300%2C300%2C-10%2C40%2C-10%2C40%2C-x%2F2%2B20%2C-x%2B30%29
.
.
2x%2B3y%3C=66
3y%3C=-2x%2B66
y%3C=-%282%2F3%29x%2B22
Graph y=-%282%2F3%29x%2B22 also.
graph%28300%2C300%2C-10%2C40%2C-10%2C40%2C-x%2F2%2B20%2C-x%2B30%2C-%282%2F3%29x%2B22%29
.
.
Find the points of intersection.
-x%2F2%2B20=-%282%2F3%29x%2B22
%28-1%2F2%2B2%2F3%29x=2
%281%2F6%29x=2
x=12
Then,
y=-12%2F2%2B20=-6%2B20=14
(12,14)
.
.
.
-x%2B30=-%282%2F3%29x%2B22
-%281%2F3%29x=-8
x=24
Then,
y=-24%2B30=6
(24,6)
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.
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The extrema of Z occur at one of these vertices.
Not sure if you need the maximum or minimum.
(0,0) : 4x%2By=4%280%29%2B0=0<-- Minimum
(0,20) :4x%2By=4%280%29%2B20=20
(12,14) :4x%2By=4%2812%29%2B14=62
(24,6) :4x%2By=4%2824%29%2B6=102
(30,0) : 4x%2By=4%2830%29%2B0=120<-- Maximum

Answer by chawki(7) About Me  (Show Source):
You can put this solution on YOUR website!
can we solve that by determinent?