Precalculus 2014
19

 PAGE: 411 SET: Exercises PROBLEM: 19

The constraints are

The objective function is .

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)

Find the value of objective function at the solution points.

At point , .

At point , .

At point , .

The object function have many solutions for different values of .

Let .

Substituite in maximum and minimum values.

.

.

.

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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