Question

Solve the linear programming problem.

Answer 1

Step 1:

The inequalities are .

Now graph the all of five constraints.

Draw the coordinate plane.

Now 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:

Step 2:

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 .

Answer 2

Contd..

Step 3:

The function

Point	Function	Value
		(Minimum)

The minimum value is at .

Solution:

The minimum value is at .