4.6-2. Consider the following problem. Maximize Z = 4x₁ + 2x₂ + 3x3 + 5X4, 2x₂ + 3x₂ + 4x3 + 2x₁ = 300 8x₁ + x₂ + x3 + 5x₁ = 300 x ≥ 0, for j = 1, 2, 3, 4. (a) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. 1 (b) Work through the simplex method step by step to solve the problem. (c) Using the two-phase method, construct the complete first sim- plex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. 1 (d) Work through phase 1 step by step. (e) Construct the complete first simplex tableau for phase 2. 1 (f) Work through phase 2 step by step to solve the problem. (g) Compare the sequence of BF solutions obtained in part (b) with that in parts (d) and (f). Which of these solutions are feasible only for the artificial problem obtained by introducing artificial variables and which are actually feasible for the real problem? c (h) Use a software package based on the simplex method to solve the problem. subject to and
4.6-2. Consider the following problem. Maximize Z = 4x₁ + 2x₂ + 3x3 + 5X4, 2x₂ + 3x₂ + 4x3 + 2x₁ = 300 8x₁ + x₂ + x3 + 5x₁ = 300 x ≥ 0, for j = 1, 2, 3, 4. (a) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. 1 (b) Work through the simplex method step by step to solve the problem. (c) Using the two-phase method, construct the complete first sim- plex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. 1 (d) Work through phase 1 step by step. (e) Construct the complete first simplex tableau for phase 2. 1 (f) Work through phase 2 step by step to solve the problem. (g) Compare the sequence of BF solutions obtained in part (b) with that in parts (d) and (f). Which of these solutions are feasible only for the artificial problem obtained by introducing artificial variables and which are actually feasible for the real problem? c (h) Use a software package based on the simplex method to solve the problem. subject to and
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:4.6-2. Consider the following problem.
Маaximize
Z = 4x, + 2x2 + 3x3 + 5x4,
subject to
2x, + 3x2 + 4x3 + 2x4 = 300
8x1 + X2 + X3 + 5x4 = 300
and
X, 2 0,
for j = 1, 2, 3, 4.
(a) Using the Big M method, construct the complete first simplex
tableau for the simplex method and identify the corresponding
initial (artificial) BF solution. Also identify the initial entering
basic variable and the leaving basic variable.
I (b) Work through the simplex method step by step to solve the
problem.
(c) Using the two-phase method, construct the complete first sim-
plex tableau for phase 1 and identify the corresponding initial
(artificial) BF solution. Also identify the initial entering basic
variable and the leaving basic variable.
I (d) Work through phase 1 step by step.
(e) Construct the complete first simplex tableau for phase 2.
I (f) Work through phase 2 step by step to solve the problem.
(g) Compare the sequence of BF solutions obtained in part (b) with
that in parts (d) and (f). Which of these solutions are feasible
only for the artificial problem obtained by introducing artificial
variables and which are actually feasible for the real problem?
c (h) Use a software package based on the simplex method to
solve the problem.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps
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,
