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

Question Description

Solve the linear programming problem by the method of corners.

Find the minimum and maximum of P = 4x + 2y subject to

3x + 5y ≥ 20 
3x + y ≤ 16
−2x + y ≤ 4
x ≥ 0, y ≥ 0. 

The minimum is P =  at 

(xy) = 
 
 
.

The maximum is P =  at 
(xy) = 
 
 
.

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Final Answer

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3x+5y>=20------------(1)

-3x-y>=-16---------(2)

2x-y>=-4------------(3)

(1)+(2)

4y>=4

y>=1

y max=1

3x+5*1=20

x>=5

x max=5


p max=4*5+2*1

=22


p min=4*0+2*0

=0

Please let me know if you need any clarification. I'm always happy to answer your questions.

sachintha (127)
UC Berkeley

Anonymous
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