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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