Docstoc

Types of Linear Programming Problem

Document Sample
Types of Linear Programming Problem Powered By Docstoc
					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


   The constrain are mutually contradictory i.e. contradict each other



  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.
      Answer: multiple optima
   2. Line z = k is ………………………………………………………… .
      Answer: objective function line
   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 ……………………………... .

Answer: infeasible

CREATE BY-NUR HIDAYAH ABD RAHMAN,PISMP MATH/BI/BM,IPGMK TENGKU AMPUAN AFZAN

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:18
posted:8/13/2012
language:English
pages:5