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The points which provides the solution to the linear programming problem max `(2x+3y)` subject to constraints `xge0, yge0, 2x+2yle9, 2x+yle6,x+2yle8` is

A

(3,2.5)

B

(2,3.5)

C

(2,2.5)

D

(1,3.5)

Text Solution

Verified by Experts

The correct Answer is:
D
let `P=2x+3y`. Graph has been shown by given constraints and maximum value of `P` can be on point A or B or C or D.

`P_(A)=P_((0,4))=2(0)+3(4)=12`
`P_(B)=P_((1,3.5))=2xx1+3xx3.5=12.5`
`P_(C)=P_((2.5,2))=2xx2.5+3xx2=11`
`P_(D)=P_((3.5,0))=2xx3.5xx3xx0=7`
Obviously `P_("max")=12.5` at `(1,3.5)`
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