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subject to X, - 2x, + x, 2 20 2x1 + 4x2 + X3 = 50 and X, 2 0, X 2 0, X3 2 0. (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. I (c) Using the two-phase method, construct the complete first simplex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial enter- ing 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.

subject to X, - 2x, + x, 2 20 2x1 + 4x2 + X3 = 50 and X, 2 0, X 2 0, X3 2 0. (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. I (c) Using the two-phase method, construct the complete first simplex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial enter- ing 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.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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4.6-7. Consider the following problem. Maximize Z = 2x, + 5x, + 3x3,
Transcribed Image Text:4.6-7. Consider the following problem. Maximize Z = 2x, + 5x, + 3x3,
subject to X - 2x, + x, 2 20 2x, + 4x2 + x3 = 50 and X1 2 0, X2 2 0, X32 0. (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. I (c) Using the two-phase method, construct the complete first simplex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial enter- ing 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.
Transcribed Image Text:subject to X - 2x, + x, 2 20 2x, + 4x2 + x3 = 50 and X1 2 0, X2 2 0, X32 0. (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. I (c) Using the two-phase method, construct the complete first simplex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial enter- ing 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.
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