# Types of Linear Programming Problem by ihzam

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```									Types of Linear Programming Problem

There are four types of linear programming problem. They are:

1. Infinitely many solutions
2. Empty feasible regions
3. Unbounded feasible regions
4. Degeneracy

1. Infinitely many solutions

 Objective function is parallel to one side of the feasible region.
 The graph below show the example situation that have infinitely many
solutions.

Multiple
optima

Lines z = k

Feasible
region
                      The linear equation of the function from the problem.
                      Line z = k is the objective function of the problem.
 Feasible region           the space that is satisfied simultaneously all the
equation in problem.
2. The Feasible Region is Empty

Example : x ≤ 2

x – y ≥ -1

x+y≥8

Solution :

1. Draw a line for the first equation (x ≤ 2). Then shade the region that is
satisfied to this equation.

y          Feasible region

X=2

x
2. Draw a line for the second equation (x – y ≥ -1). Then shade the region that is
satisfied to this equation.

y        Feasible region

X=2

Feasible region

X – y = -1

x
3. Then, draw a line for the second equation (x + y ≥ 8). Then shade the region
that is satisfied to this equation.

y        Feasible region

X=2

Feasible region

X – y = -1

Feasible region
X +y = 8

x

4. We can see that there is no region that is satisfied simultaneously for all the
equation of the linear programming problem.
5. So that, we define this situation as empty feasible regions.
6. This situation is also said to be infeasible.
Example Question

a) Answer the question according to the graph below.

Lines z = k

Feasible
region

1. Fill in the blank in the graph above.
2. Line z = k is ………………………………………………………… .
3. Feasible region is ………………………………………………………………….. .
Answer: the space that is satisfied simultaneously all the equation in
problem
4. We can say that the problem is empty feasible region when ……………………
………………………………………………………………………………………… .
Answer: there is no region that is satisfied simultaneously for all the
equation of the linear programming problem
5. The empty feasible region is also could be said as ……………………………... .