SOLUTION: Find the minimum and maximum values of z=2x+3y if possible, for the following set of constraints x+y≤9 -x+y≤5 2x-y≤14 Find minimum value & maximum value.

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Question 323823: Find the minimum and maximum values of z=2x+3y if possible, for the following set of constraints
x+y≤9
-x+y≤5
2x-y≤14
Find minimum value & maximum value.
Please help! :)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the feasible region using the constraints.
Find the intersection points.
9-x=5%2Bx
2x=4
x=2
y=7
(2,7)
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9-x=2x%2B14
3x=-5
x=-5%2F3
y=9-%28-5%2F3%29=32%2F3
(-5/3,32/3)
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2x%2B14=5%2Bx
x=-9
y=5-9=-4
(-9,-4)
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The min and max of the function will occur at one of the vertices:
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(2,7):z=2x%2B3y=2%282%29%2B3%287%29=25
(-5/3,32/3):z=2x%2B3y=2%28-5%2F3%29%2B3%2832%2F3%29=86%2F3
(-9,-4):z=2x%2B3y=2%28-9%29%2B3%28-4%29=-30
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The min value of z of -30 occurs at (-9,-4).
The max value of z of 86/3 occurs at (-5/3,32/3).