SOLUTION: Solve the following Linear Programming problem using the corner point method. Maximize - 3X + 5Y Subject to - 4X + 4y <=48

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Question 322796: Solve the following Linear Programming problem using the corner point method.
Maximize - 3X + 5Y
Subject to -
4X + 4y <=48
X + 2Y <=20
X,Y >= o
a) Plot the graph for each
b) Find the four corner points
c) Find the profit for each Point
d) What is the maximum profit?
My answer:
Graph 4x + 4y <= 48 Graph x + 2y = 20
X= 0 y=12 x= 0 y= 10
x= 0 y= 12 x = 20 y= 0
I have done the graph but I do not know how to work the rest


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following Linear Programming problem using the corner point method.
P%28x%2Cy%29=3x+%2B+5y


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The feasible region (shown by the blue polygon) is formed from the two lines and the two axes. The intersection of the lines with the axes give two points, the intersection of the axes (0,0) gives a third point.
You also need to find the intersection of the two lines to get the fourth point in the feasible region:
y=12-x and
y=%2820-x%29%2F2
which occurs at (4,8).
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c)The maximum and minimum for P(x,y) occurs at one of the vertices.
Calculate the value at each of them,
(0,0):P=3x%2B5y=0
(12,0):P=3x%2B5y=3%2812%29=36
(0,10):P=3x%2B5y=5%2810%29=50
(4,8):P=3x%2B5y=3%284%29%2B5%288%29=52
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d)The maximum profit of 52 occurs when x=4 and y=8.