Question

what is the minimum value for z=3x-1/2y over the feasibility region defined by the constraints?
a.-4
b.-5
c.-3
d.-6

Answer 1

not knowing the constraints, it's hard to say.

Answer 2

constraints
x greater than or equal to 0
y less than or equal to 8
y greater than or equal to x
y greater than or equal to -1/2x+6

Answer 3

there is a handy tool at

http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html

Just visit there and enter

minimize z = 3x - (1/2)y subject to
y <= 8
x - y <= 0
(1/2)x + y >= 6

set the limits as
-10 <= x <= 10
0 <= y <= 20

hit Solve for the solution
hit Graph for a nice picture of the region