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

MB0048, A paper mill produces two grades of paper viz., X and Y. Because of...

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

Macroeconomic environment in which the business operates, Provide a descrip...

Provide a description of the macroeconomic environment in which the business operates noting: a) The overall 'stability' of the political system/government of the country in whi

Mathematical, Ask 7:23 PM Docx Reader GROUP-7 1. A firm manufactures two pr...

Ask 7:23 PM Docx Reader GROUP-7 1. A firm manufactures two products A & B on which the profits earned per unit is Rs.3 and Rs.4. Each product is processed on two machines Miand M2.

Least cost methods, The NW  corner  rule  described  earlier considers only...

The NW  corner  rule  described  earlier considers only  the availability  and supply  requirements  in making  assignments. It takes  no account  of the shipping  costs  given  in

Quartiles, QUARTILES The three points on the scale  of observation ( o...

QUARTILES The three points on the scale  of observation ( or  values  of the variable) which  divide  the total  frequency  into four  equal  parts are called  quartiles for t

Mk, Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = ...

Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0

Linear programming model, Nass food produces to kinds of popular dark choco...

Nass food produces to kinds of popular dark chocolate bars. The banana and the coffee.the

Z-test - hypothesis testing, Z-Test Prof. Fisher has  given a method  of...

Z-Test Prof. Fisher has  given a method  of testing the significance of the correlation coefficient in small  samples. According  to this method the  coefficient of correlation

Linear Programming, b. A paper mill produces two grades of paper viz., X an...

b. 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 pape

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