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11

Step-by-step Answer
PAGE: 782SET: ExercisesPROBLEM: 11
Please look in your text book for this problem Statement

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 image and it occurs at image.

The minimum value is image at image.



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