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.

The point is not considered as .

Observe the graph,

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

System of boundary equations |
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Solution (vertex points) |

Find the value of objective function at the solution points.

At point , .

At point , .

At point , .

At point , .

Observe the values of ,

The maximum value of is when and .

The minimum value of is when and .

The maximum at point is .

The minimum at point is .

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