​Solve the linear programming problem by the method of corners.

Mathematics
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Solve the linear programming problem by the method of corners.

MaximizeP = x + 4y    
subject to  x + y ≤
2x + y ≤6
x ≥ 0, y ≥ 0

The maximum is P =  at 
(xy) = 
 
 
.
Jun 4th, 2015

Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

The corners of the feasible region are (0,0), (3,0), (2,2) and (0,4) 

Lastly, we simply evaluate the function P = x + 4y at each of the corners and see which value is biggest. Checking them all gives: 

P(0,0) = 0 
P(0,4) = 16 
P(2,2) = 10 
P(3,0) = 3 

So the maximum value for P occurs at corner (0,4)

the maximum value is p= 16 at (x,y)= (0,4)

Please let me know if you need any clarification. I'm always happy to answer your questions.Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 4th, 2015

What would the minimum at P be? 0? at what point?

Jun 4th, 2015

P=0 at (0,0)

Jun 4th, 2015

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