#### Answer

The maximum of the objective function is 610.
The minimum of the objective function is 0

#### Work Step by Step

See: Solving a Linear Programming Problem (p.577).
If a maximum or minimum value of exists, it can be determined as follows:
1. Graph the system of inequalities representing the constraints.
2. Find the value of the objective function at each corner, or vertex of the graphed region.
The maximum and minimum of the objective function occur at one or more of the corner points
----------------
Set up a table (see below, desmos.com ),
calculating $z(x,y)$ for each corner point.
The maximum of the objective function is 610.
The minimum of the objective function is 0