Question 148088: The maximum value of z = 20x + 8y subject to:
3x + y ≤ 24
6x + 4y ≤ 66
x ≥ 0, y ≥ 0
a. 220
b. 160
c. 172
d. 132
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! Solve the auxiliaries for y first.
y<=24-3x
y<=33/2 -3x/2
Now, if y>=0,
24-3x >=0
33/2 - 3x/2 >=0
Moreover,
if x>=0,
-3x>=-24
-3x/2>=-33/2
Even further,
x<=8
x<=11
So the maximum of x will be 8.
Now,
y<=0 follows from the first condition with restriction x<=8. So the maximum of y will be 0.
Thus,
z=20x + 8y
z=20*11=220
Which is answer (a).
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