Question 221527: Can someone explain to me how to maximize by the simplex method? I get confused after the second step.
Here is the problem,
Maximize P=0.3x ++ 0.4y
Subject to: 4x + 8y equals or less than 1600
12x+8y equal or less than 1920
x equal to or greater than 0; y equal to or greater than 0
Please help me. I know how to do the first step of charting but the second step on confuses me? How do I decide which negative should be the pivot point?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Here is the problem,
Maximize P=0.3x ++ 0.4y
Subject to:
4x + 8y equals or less than 1600
12x+8y equal or less than 1920
x equal to or greater than 0; y equal to or greater than 0
Please help me. I know how to do the first step of charting but the second step on confuses me? How do I decide which negative should be the pivot point?
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Solve each of the inequalities for "y"
y <=(-1/2)x + 200
y <= (-3/2)x + 240
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Plot those boundary lines and the intersecting solution regions.
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Find the corners of the solution region:(0,0),(0,200),(40,180),(160.0)
----------------------
Check each of those number pairs in P=0.3x + 0.4y
to determine which pair give you the maximum "p" value.
(0,0) gives P = 0
(0,200) gives p = 0 + 0.4*200 = 80
(40,180) gives p = 0.3*40 + 0.4*180 = 84
(150,0) gives p = 0.3*150 + 0 = 45
--------------------------------------------
So (40,180) gives the maximum Profit.
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Cheers,
Stan H.
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