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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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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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.
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.
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