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, x2  ≥ 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, a2  ≥ 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, a2  ≥ 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 prouduces two grads of paper viz., X and ...

A paper mill prouduces two grads of paper viz., X and Y. Becouse of raw material restriction, it cannot product more then 400 tons of grade X paper and 300 tons of grade Y paper in

Pay-off matrix , In a rectangular game, pay-off matrix of player A is as fo...

In a rectangular game, pay-off matrix of player A is as follows: Player B B1 B2 Player A A1 A2 i) Solve the game. ii) Write down the pay-off matrix of B and th

Operation research, Operations research is used by manager in making busine...

Operations research is used by manager in making business decisions. What are five each of its merit and demerit that the users need to be aware of?

Determine the optimal assignment., #questiSix Operators are to be assigned ...

#questiSix 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 ass

Lpp, Determine feasible space for x1-x2= 8

Determine feasible space for x1-x2= 8

Simplex method LPP, #questioA paper mill produces two grades of paper viz.,...

#questioA 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

Non parametric tests - hypothesis testing, NON PARAMETRIC TESTS All  ...

NON PARAMETRIC TESTS All  practical  data follow normal distribution under  such situations can estimate the  parameters such  as mean  variance etc ,,, and use the  standard

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