Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 4.5, Problem 3P

Explanation of Solution

Simplex algorithm

  • x1, x2, s1, s2 and s3 are the basic variables.
  • For solving a linear problem using simplex algorithm, first the linear problem is converted to its standard form.
  • The RHS is the right hand side of the constraints in the linear problem.
  • Then a basic feasible solution is found which is easy if all the constraints are less than or equal with non-negative right hand side.
  • If all nonbasic variables have nonnegative coefficients in row 0 then that basic feasible solution is optimal.
  • If any variable have negative coefficient in row 0 then the variable with the most negative coefficient is chosen to enter the basis.
  • If one or more constraints have a negative right hand side then there is no longer a basic feasible solution.
  • After the iteration one, the initial table is
z x1 x2 x3 s1 s2 s3
1 -2 1 -1 0 0 0
0 3 1 1 1 0 60
0 1 -1 2 0 1 0
0 1 1<

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Chapter 4 Solutions

Introduction to mathematical programming

Chapter 4.5, Problem 1P Chapter 4.5, Problem 2P Chapter 4.5, Problem 3P Chapter 4.5, Problem 4P Chapter 4.5, Problem 5P Chapter 4.5, Problem 6P Chapter 4.5, Problem 7P Chapter 4.6, Problem 1P Chapter 4.6, Problem 2P Chapter 4.6, Problem 3P Chapter 4.6, Problem 4P Chapter 4.7, Problem 1P Chapter 4.7, Problem 2P Chapter 4.7, Problem 3P Chapter 4.7, Problem 4P Chapter 4.7, Problem 5P Chapter 4.7, Problem 6P Chapter 4.7, Problem 7P Chapter 4.7, Problem 8P Chapter 4.7, Problem 9P Chapter 4.8, Problem 1P Chapter 4.8, Problem 2P Chapter 4.8, Problem 3P Chapter 4.8, Problem 4P Chapter 4.8, Problem 5P Chapter 4.8, Problem 6P Chapter 4.10, Problem 1P Chapter 4.10, Problem 2P Chapter 4.10, Problem 3P Chapter 4.10, Problem 4P Chapter 4.10, Problem 5P Chapter 4.11, Problem 1P Chapter 4.11, Problem 2P Chapter 4.11, Problem 3P Chapter 4.11, Problem 4P Chapter 4.11, Problem 5P Chapter 4.11, Problem 6P Chapter 4.12, Problem 1P Chapter 4.12, Problem 2P Chapter 4.12, Problem 3P Chapter 4.12, Problem 4P Chapter 4.12, Problem 5P Chapter 4.12, Problem 6P Chapter 4.13, Problem 2P Chapter 4.14, Problem 1P Chapter 4.14, Problem 2P Chapter 4.14, Problem 3P Chapter 4.14, Problem 4P Chapter 4.14, Problem 5P Chapter 4.14, Problem 6P Chapter 4.14, Problem 7P Chapter 4.16, Problem 1P Chapter 4.16, Problem 2P Chapter 4.16, Problem 3P Chapter 4.16, Problem 5P Chapter 4.16, Problem 7P Chapter 4.16, Problem 8P Chapter 4.16, Problem 9P Chapter 4.16, Problem 10P Chapter 4.16, Problem 11P Chapter 4.16, Problem 12P Chapter 4.16, Problem 13P Chapter 4.16, Problem 14P Chapter 4.17, Problem 1P Chapter 4.17, Problem 2P Chapter 4.17, Problem 3P Chapter 4.17, Problem 4P Chapter 4.17, Problem 5P Chapter 4.17, Problem 7P Chapter 4.17, Problem 8P Chapter 4, Problem 1RP Chapter 4, Problem 2RP Chapter 4, Problem 3RP Chapter 4, Problem 4RP Chapter 4, Problem 5RP Chapter 4, Problem 6RP Chapter 4, Problem 7RP Chapter 4, Problem 8RP Chapter 4, Problem 9RP Chapter 4, Problem 10RP Chapter 4, Problem 12RP Chapter 4, Problem 13RP Chapter 4, Problem 14RP Chapter 4, Problem 16RP Chapter 4, Problem 17RP Chapter 4, Problem 18RP Chapter 4, Problem 19RP Chapter 4, Problem 20RP Chapter 4, Problem 21RP Chapter 4, Problem 22RP Chapter 4, Problem 23RP Chapter 4, Problem 24RP Chapter 4, Problem 26RP Chapter 4, Problem 27RP Chapter 4, Problem 28RP
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