Step 1:

The objective function is .

The constraints are

.

Graph :

Graph the inequalities and shade the required region.

Note : The shaded region is the set of solution points for the objective function.

Observe the graph:

Tabulate the solutions of each of two system of inequalities and obtain the intersection points.

\ System of boundary \ equations \	\ \ \	\ \ \	\ \ \	\ \ \	\ \ \
Solution (vertex points)					\ \

Step 2:

Find the value of objective function at the solution points.

The objective function is .

At point : .

At point : .

At point : .

At point : .

At point : .

Observe the values of :

The maximum value of is when and .

Solution:

The maximum at point is .