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

Linear programming , A paper mill produces two grades of paper viz., X and ...

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

LP - Assignment problem, I have looked at Hungarian algorithm to solve assi...

I have looked at Hungarian algorithm to solve assignment problem, but it seems like it is limited to 1-to-1 assignment. I would like to know how to do 1-to-3 assignment.

General rules, General Rules a. Attractive Shapes The tables  should ...

General Rules a. Attractive Shapes The tables  should be  neat  and  attractive. The size of  table  should be neither too big nor  small. b. Simplicity A table  should b

OR models, Explain why it may be advantageous to build models to help in so...

Explain why it may be advantageous to build models to help in solving a decision problem.

Markert reseach, The Upjohn Company, based in Kalamazoo, Michigan, manufact...

The Upjohn Company, based in Kalamazoo, Michigan, manufactures and markets pharmaceuticals and health-related products. With more than 19,000 employees and distribution in over 30

Mean deviation - measure of dispersion, MEAN DEVIATION Mean  deviati...

MEAN DEVIATION Mean  deviation of a series is the arithmetic  average of the  deviations of various  items  from the  median  or mean  of that series. Median is preferred

ASSIGNMENT ANSWER, Six Operators are to be assigned to five jobs with the c...

Six Operators are to be assigned to five jobs with the cost of assignment in Rs. given in the matrix below. Determine the optimal assignment. Which operator will have no assignment

Steps involved in linear programming problem formulation, Question A - Line...

Question A - Linear Programming is most widely used technique for large number of applications in business industry as well as in various other fields. Describe in brief the steps

test statistic - hypothesis testing , Test Statistic The next  step ...

Test Statistic The next  step is compute an appropriate  test statistic which  is based on an appropriate probability distribution. It  is used to test whether the null  hypo

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