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
To find the minimum value of z, you need to evaluate the objective function (z = 3x - (1/2)y) at each corner point of the feasibility region defined by the constraints and determine which one gives you the smallest value.
However, since you haven't provided the constraints, I cannot determine the exact feasibility region. Please provide the constraints so that I can assist you further and determine the minimum value of z.
not knowing the constraints, it's hard to say.
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
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