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To maximise the objective function z=x+2...

To maximise the objective function `z=x+2y` under the constraints `x-y le 2, x+yle4 and x,yge0` is

A

1x=0,y=4,z=8`

B

`x=1,y=2,z=5`

C

`x=1,y=4,z=9`

D

`x=0,y=3,z=6`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `x-y=2implies(x)/(2)+(y)/(-2)=1`
This line meets the exes at (2,0) ltbRgt and (0,-2).

No x+y=14
`implies(x)/(4)+(y)/(4)=1`
This line meets the axes at (4,0)
and (0,4). Now, at point (0,4), z=0+4`xx`2=8
at point `(2,0),z=2+0=2`
and at point `(3,1),z=3+2=5`
Thus, function is maximum at (0,4) and maximum value is 8.
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