SOLUTION: maximize Z=8x+7y subject to 3x+y≤66 ,x+y≤45 ,x≤20 ,y≤40,x,y≥0

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Question 1023175: maximize Z=8x+7y subject to 3x+y≤66 ,x+y≤45 ,x≤20 ,y≤40,x,y≥0
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
Solution by the graphical method. (Typesetting here of simplex method would be brutal. The graphical method is a little less difficult, but the region of feasibility will not be reproduced.)
The region of feasibility would be a hexagon (six-sided) figure with the following corner points (in ccw direction):
(0,0), (20,0), (20,6), (21/2,69/2), (5,40), and (0,40).
For (0,0), Z = 0
For (20,0), Z = 8*20 = 160
For (20,6), Z = 202
For (21/2,69/2), Z = 325.5
For (5,40), Z = 320, and
For (0,40), Z = 280
By the fundamental theory of linear programming the maximum exists at the point (21/2,69/2) with a Z value of 325.5.
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