The inequalities are .

Now graph the all of five constraints.

Draw the coordinate plane.

Now the inequality .

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• Graph the line .
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•  Since the inequality symbol is the boundary is included the solution set.
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• Graph the boundary of the inequality with solid line.
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• To determine which half plane to be shaded use a test point in either half- plane.
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• A simple choice is . Substitute in original inequality.
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The statement is false.

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• Since the statement is false, shade the region does not contain point .
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Similarly graph the other inequalities.

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• Second inequality
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Test point

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

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• Third inequality
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Test point

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

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• Fourth inequality
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Test point

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

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• Fifth inequality .
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Test 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  .