\ \

The inequalities are . \ \

Graph the all of four 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 true. \ \

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

Similarly graph the other inequalities. \ \

The inequality. \ \

Test point is \ \

\ \

. \ \

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

The inequality . \ \

Test point \ \

\ \

. \ \

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

The inequality . \ \

Test point \ \

\ \

. \ \

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

Graph : \ \

\ \

\ \

Graph : \ \

The feasible area looks like in the graph as \ \

\ \

Observe the graph the corner points are , , and . \ \

The function is .

Point	\ Function \	\ Value \
	\ \	\ (maximum) \
\ \	\ \	\ \
\ \	\ \	\ \
	\ \	\ \

The maximum value of is and it occurs at  . \ \

The maximum value of is at .