For the following linear programming problem minimize `Z=4x+6y` subject to the constraints `2x+3yge6,x+yle8,yge1,xge0`, the solution is

Options

A. (0, 2) and (1, 1)
B. (0, 2) and `((3)/(2),1)`
C. (0, 2) and (1, 6)
D. (0, 2) and (1, 5)

Answer

B

Explanation

Given, `Z=4x+6y`
The minimum point of Z can be on
A, B, C and D.

Now, `Z_(A)=Z_((3//2","1))=4((3)/(2))+6(1)`
`=6+6=12`
`Z_(B)=Z_((0", "2))=4(0)+6(2)`
`=0+12=12`
`Z_(C)=Z_((7", "1))=4(7)+6(1)`
`=28+6`
`=34`
and `Z_(D)=Z_((0", "8))=4(0)+6(8)`
`=0+48=48`
`:.` Z minimum at the point `((3)/(2),1)` and (0, 2).