Graph the feasible set of the system of linear inequalities. shade the feasibility region

Question

x+2y>(or =to)4

2x-y>(or=to)6

 

 

 

and ,

2x+3y<(or=to)9

x+y<(or=to)4

x>(or=to)1 , y>(or=to)0

Answer 1

(a)

Step 1:

The system of inequalities are and .

Draw the coordinate plane.

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute in .

.

The statement is true.

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

Step 2:

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute in .

.

The statement is true.

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

Graph:

Graph the inequalities: and .

Shade the required region.

Step 3:

Feasible Region:

The graph of the inequalities and is the shaded region, where every point in the shaded region satisfies the both the inequalities.

Graph:

Shade the feasible region:

Solution:

Graph of the region bounded by the system of inequalties is

.

Answer 2

(b)

Step 1:

The system of inequalities are  and .

Graph the all of four constraints.

Draw the coordinate plane.

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute  in .

.

The statement is true.

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

Step 2:

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute  in .

.

The statement is true.

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

Step 3:

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute  in .

.

The statement is true.

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

Comments

Contd...

Step 4:

Consider 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 is to be shaded, consider a test point in either of the half- plane.

Test point is .

Substitute  in .

.

The statement is true.

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

Graph:

Graph the inequalities:  and .

Shade the required region.

Step 5:

Feasible Region:

The graph of the inequalities and is the shaded region, where every point in the shaded region satisfies the all inequalities.

Graph:

Shade the feasible region:

Solution:

Graph of the region bounded by the system of inequalties is