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

Assignment Help:

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


Related Discussions:- Linear programming solution by steps for two-phase method

Determine capacity of unit, Show simple vapour compression Refrigeration cy...

Show simple vapour compression Refrigeration cycle with showing all the devices and also draw T-sand P-R diagram and illustrate it also. A Bell-Coleman cycle works between 1 bar

Simple random sampling - sampling decisions, Simple Random Sampling  ...

Simple Random Sampling  This  is  simplest  and most  popular  technique  of sampling. In it each  unit  of the  population has equal  chance  of being  included in the samp

Manufacturing operation , You are a manager at a medium sized manufacturing...

You are a manager at a medium sized manufacturing operation that sells a customized product directly to the consumers and the data pattern is linear but it can have the occasion ra

What do you mean by linear programming problem, Q1. a. What do you mean by ...

Q1. a. What do you mean by linear programming problem? Explain the steps involved in linear programming problem formulation? b. A paper mill produces two grades of paper viz., X

information on research done, Information on Research Done Informatio...

Information on Research Done Information on Doctoral research work already done  is available from  the followings  sources: a. Bibliography of Doctoral  Dissertations Acce

Inflation, Inflation Inflation is a general...

Inflation Inflation is a general increase in the price of goods and services. The inflation rate, as measured by the

Scattered responsibility and authority, Scattered Responsibility and Autho...

Scattered Responsibility and Authority: In a big industry responsibility and authority of decisions making is scattered throughout the organization and thus the organization.

Calculate, A paper mill produces two grades of paper viz X and Y. Because o...

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 in

CHARACTERISTIC, O.R REPLACES MANAGEMENT BY PERSONALITY

O.R REPLACES MANAGEMENT BY PERSONALITY

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd