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.

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 $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

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

The maximum value of $\"\"$ is $\"\"$ at $\"\"$ .