SOLUTION: Find the maximun value of z=3x +2y subject tothe contraints x>=0, y>=0, x+2y<=4, x-y<=1

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Question 108332: Find the maximun value of z=3x +2y subject tothe contraints x>=0, y>=0, x+2y<=4, x-y<=1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can find the feasible region that the constraints apply to by graphing.
Plot the two lines x-y=1 and x%2B2y=4 and determine which region is appropriate and remember the other two constraints x%3E=0 and y%3E=0.

The graph shows the blue region bounded by the four corners.
From linear programming, the max and min values of your function occur on the corners.
Let's calculate the values at each corner.
The corners are (0,0), (1,0), (0,2), and (2,1).
z=3x +2y=3(0)+2(0)=0
z=3x +2y=3(1)+2(0)=3
z=3x +2y=3(0)+2(2)=4
z=3x +2y=3(2)+2(1)=8
The max value is 8 and it occurs at (2,1).