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Z=30x +20 y , x+y le 8, x +2y ge 4,6x +4...

`Z=30x +20 y` , `x+y le 8, x +2y ge 4,6x +4 ge 12,x ge 0 ,y ge 0 `

A

unique solution

B

infinitely many solution

C

minimum at (4, 0)

D

minimum 60 at point (0, 3)

Text Solution

Verified by Experts

The correct Answer is:
B
Feasible region is ABCDFA
and Z = 30 x + 20 Y

Now, at `A(4,0) , Z= 30 xx 4 +0 = 120`
`B(8,0)Z = 30 xx 8+0 = 240 `
`C(0,8) , Z=0 +20 xx 8 = 160 ` ,brgt ` D(0,3), Z =0 +20 xx 3 = 60 ` (Minimum) and ` F(1,3/2)`
`Z = 30 xx 1+20 xx 3/2 = 60 ` (Maximum)
it is clear that minimum vlaue of Z is 60 at pionts D(0,3) and ` F(1,3/2)` . So, minimum vlaue of Z is obtained at every point of the line segment DF. Hence infinitely many solutions exist .
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