Linear programming solution by steps for two-phase method, Operation Research

Solve by Steps for Two-Phase Method

Max Z = 5x1 + 8x2

Subject to

3x1 + 2x2 ≥ 3

x1 + 4x2 ≥ 4

x1 + x2 ≤ 5

    &     x1 ≥ 0, x≥ 0

Answer

Standard LPP

 

Max Z = 5x1 + 8x2  

    Subject to

                        3x1 + 2x2 - s1+ a1 = 3

                        x1 + 4x2 - s2+ a2  = 4

                        x1 + x2 + s3 = 5

                        x1 , x2 , s1, s2, s3, a1, a≥ 0

 

Auxiliary LPP

Max Z* = 0x1 + 0x2 + 0s1 + 0s2 + 0s3 -1a1 -1a2

    Subject to

                        3x1 + 2x2 - s1+ a1 = 3

                        x1 + 4x2 - s2+ a2  = 4

                        x1 + x2 + s3 = 5

                        x1 , x2 , s1, s2, s3, a1, a≥ 0

1377_two-steps-method-LPP.png

 

As all Δj ≥ 0, Max Z* = 0 and no artificial vector appears in the basis, we move to phase II. 

Phase II

266_phase-II.png

As all Δj ≥ 0, optimal basic feasible solution is achieved. Thus the solution is Max Z = 40, x1 = 0, x2 = 5

Posted Date: 7/8/2012 12:36:46 AM | Location : United States







Related Discussions:- Linear programming solution by steps for two-phase method, Assignment Help, Ask Question on Linear programming solution by steps for two-phase method, Get Answer, Expert's Help, Linear programming solution by steps for two-phase method Discussions

Write discussion on Linear programming solution by steps for two-phase method
Your posts are moderated
Related Questions
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

minimization

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2

is model the essence of oprational research.

Line Balancing Methods - Heuristic Approach  Heuristic mean serving to find i.e. to find out discover things for oneself. Heuristic describes a particular approach to problem so

Cost- sampling decisons                         σ x¯ =S/√n       Where is the  standard  error of he mean is the standard devaluation of  the population and n is t

The systematic methodology developed for an operation research study with problems involving conflicting multiple objective policies and alternatives. Operation research in

In a big industry the numbers of factors influencing a decision have increased situation has become big and complex because these factors interact with each other in complica

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

how the sequencing techniques help the manager