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

Question

I understand how to graph this. I also know where the feasible region is. I'm just having trouble identifying exactly how to find the z co-ords. Would very much appreciate the help!

Constraints: 2x-y≤12, 4x+2y≥, and x+2y≤6.

Optimization Equation: z=2x+5y

Answer 1

Assuming that you have drawn a graph of the feasibility region, just make a list of the coordinates of the corner points. Then calculate the value of the optimization equation (z) at each corner point.

The highest value of z throughout the feasibility region will be the corner point with the highest z. The lowest value of z throughout the feasibility region will be the corner point with the lowest z.