Given the following constraints, find the maximum and minimum values for z . please help

Question

Constraints: 

2x−y≤12

4x+2y≥0

x+2y≤6

Optimization Equation: z=2x+5y

Maximum Value of z:

Minimum Value of z:

Answer 1

Graph the constraint inequalities (including the shaded regions. You will get on "intersection" that looks like this:

Point A is (-2, 4)

Point B is (6, 0)

Point C is (3, -6)

Now, plug each point into the optimization equation z = 2x + 5y

For point A: z = 2(-2) + 5(4) = 16

For point B: z = 2(6) + 5(0) = 12

For point C: z = 2(3) + 5(-6) = -24

So the max value of z is 16 and the min value of z is -24