Pre-Calculus, 9th edition
11

 PAGE: 782 SET: Exercises PROBLEM: 11

The inequalities are .

Graph the all of five constraints.

Draw the coordinate plane.

The inequality.

Graph the line .

Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is false.

Since the statement is false, shade the region does not contain point .

Similarly graph the other inequalities.

The inequality.

Test point

Since the statement is true, shade the region contain point .

The inequality .

Test point

Since the statement is true, shade the region contain point .

The inequality .

Test point

Since the statement is true, shade the region contain point .

The inequality .

Test point

.

Since the statement is true, shade the region contain point .

Graph:

The feasible area looks like in the graph.

To find minimum value we need to use corner point theorem.

From the graph the corner points are .

The function   .

 Point Function Value (Minimum)

The minimum value of is and it occurs at .

The minimum value is at .

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