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Minimise z=3x+y, subject to 2x+3yle6,x+y...

Minimise `z=3x+y`, subject to `2x+3yle6,x+yge1, xge0,yge0`

A

`x=1,y=1`

B

`x=0,y=1`

C

`x=1,y=0`

D

`x=-1,y=-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Since `2x+3y=6`
`impliesx/3+y/2=1`

This line meets the axes at (3,0) and (0,2).
Now `x+y=1`
Thisline meet theaxes at (1,0) and (0,1).
Now at `A(1,0),z=3`
at `B(3,0),z=9` at `C(0,1),Z=1`
at `D(0,2),Z=2`
So it is clear the minimum value of `z` at (0,1).
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