Solve the following problems with the two-phase simplex method. For each problem,show your solution to each of the following steps.(a) Transform the original LP into an LP to which phase l of the simplex methodcan be applied.(b) Formulate an artificial LP (ALP) that is solved in phase 1. Use as fewartificial variables as possible.(c) Carry out phase 1 on the ALP using the simplex method.(d) Clearly state an optimal solution and the optimal objective value to theALP.(e) Based on your answer to part (d), draw a conclusion about the feasibility ofthe original LP.(f) Form the initial tableau for phase 2.(g) Obtain the canonical form corresponding to the current basic solution tothe original LP.(h) Carry out phase 2 of the simplex method on the original LP.(i) Clearly state an optimal solution and the optimal objective value to theoriginal LP.22. Maximize z =subject toX1 +x2-X3 + x+x5 32x1-x2 + x3 - 2x4%3D3x1- x3 + 3x4X; 2 0, j= 1,2,3, 4.2)2.

Answered: Image /qna-images/answer/ca7bdca5-5fee-494d-8e49-24609077e927.jpg

Answered: Solve the following problems with the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Solve the following using Simplex Method. 1. A factory makes three types of chairs, A, B, and C. The factory makes a profit ci P200 on chair A, P300 on chair B, and P400 on chair C. Chair A requires 30 man-hours, chair B requires 20, and chair C requires 10. Chair A needs 2m2 of wood, chair needs 5m2, and chair C needs 3m2. Given 100 man-hours and 15m2 of wood per week, how many chairs of each type should be made each week to maximize profit? 2. Maximize Z = 8x +6 x Subject to: 10x,+ X2s 12 2xi+ 5 x2s 16 X120 INH
Question 3 Consider the following LP problem: МАX 40X, + 50X2 Subject to: Х, + 2X, S 40 4X1 + 3X2 s 120 X1, X2 2 0 a) Create the initial simplex tableau
Over at Duffin House, Marjory Duffin is trying to decide on the size of the print runs for the best-selling new fantasy novel Larry Plotter and the Simplex Method. The following model shows a calculation of the total cost to produce a million copies of the novel, based on an analysis of setup and storage costs c(n) = 0.0008n² - 74n+ 2,000,000 dollars, where n is the print run size (the number of books printed in each run). (a) What would be the effect on cost if the run size was increased from 20,000 to 30,000? A run of size 20,000 would cost $ and a run of 30,000 would cost $ dollars. $30,000 per month would result in a savings of Thus, increasing the run size from $20,000 to (b) Would increasing the run size in further steps of 10,000 result in the same changes in the total cost? Explain. O The cost decreases at a faster and faster rate and then begins to increase. Going from 30,000 to 40,000 decreases the cost by about the same a going from 20,000 to 30,000. O The cost decreases at…
Can you show how to get to these answers.
Work through the simplex method (in algebraic form) step by step to solve the following problem. Maximize Z = x1 + 2x2 + 2x3, subject to 5x1 + 2x2 + 3x3 ≤ 15 x1 + 4x2 + 2x3 ≤ 12 2x1+ x3 ≤ 8 and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
Consider the simplex tableau given below. X1 X2 S2 S3 1 4 1 12 0. 1 5 - 6 - 2 1 4 (A) The pivot element is located in column and row . (B) The entering variable is (C) The exiting variable is (D) Enter the values after one pivot operation in the tableau below. X1 X2 S1 S2 S3 P 0.2 0.4 1 - 0.4 3.2 1 10 0. 1 1.2 0.4 0. (Type an integer or a decimal.) Enter your answer in each of the answer boxes. Poo0 N O
Q6 (a) Use Gauss-Seidel Method to obtain the solution of the following system: 0.4х, — (2 + 1)х, + 1.5х, — 4.56 - (3 + 1)x, + 0.2x, -1.9x, = 1.73 2.5x, –1.6x, + (3+ Iſx,= 8.45 - Stop the iteration until max {]xk+1 – x} < 0.003.
A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. In how many days will A,B,C finish it, working togeteher? In hpw many days will each one of them finish it, working alone?
Use the simplex method to solve the following simplex problems. a) Maximise 6x1 + 9x2 + 6x3 subject to 3x1 + 2x2 + x3 = 0.
Solve the following LPP problems using Simplex Method: 4. Max Z = X1 - 3 X2 + 2x3 Subject to 3x1 - X2+ 2x3 =0
5. Derive the formula for Adams-Moulton Three-Step Implicit Method h Yi+1 = Y; + + 12/24 (9fi+1 +19fi − 5fi-1 + f₁-2).
Consider the following LP model: max 10x1 + 12x2 + s.t. x1 2x1 2x1 + + + X2 + 2x2 + 2x3 + 2x3 2x2 + X3 X 12x3 ≤20 0 Use the simplex method and find the optimal solution for this problem. (You need to determine the objective value, the basic and non-basic variables and their values.)

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS