Operation Research 5: Linear Programming Solution Simplex Method, Maximization problem

TL;DR

Learn how to solve linear programming problems with three decision variables using the simplex method for maximization.

Transcript

hello everybody and welcome to lesson 5 linear programming solution using simplex method in the case of maximization previously as you remember we have discussed about linear programming solution using graphical method by the way graphical method can solve linear programming having two decision variables if the decision variables are more than two ... Read More

Key Insights

• ❓ The simplex method is used to solve linear programming problems with more than two decision variables.
• ❓ It is an iterative process that starts with an initial feasible solution and improves it with each iteration.
• 🤨 The steps of the simplex method include converting inequalities to equalities, creating the simplex tableau, determining the pivot column and row, pivoting, and checking for optimality.
• ↗️ The pivot column is determined by the most positive entry in the cj - zj row, while the pivot row is determined by the smallest positive ratio of the right hand side column to the pivot column.
• 💄 Pivoting involves making the pivot value 1 and the remaining entries in the pivot column 0.
• ❓ The process continues until an optimal solution is reached, where the objective function is maximized.
• ↘️ The final solution can be found in the lower right corner of the final tableau.

Questions & Answers

Q: What is the difference between the graphical method and the simplex method in solving linear programming problems?

The graphical method can only solve problems with two decision variables, while the simplex method is used for problems with more than two decision variables.

Q: How does the simplex method determine the pivot column?

The pivot column is determined by locating the most positive entry in the cj - zj row, where cj is the coefficient of the decision variable and zj is the product of the coefficients of the basic variables with the corresponding column entries.

Q: What is the pivot row and how is it determined?

The pivot row is determined by finding the smallest positive ratio of the right hand side column to the pivot column. The row with this ratio is selected as the pivot row.

Q: What is the purpose of pivoting in the simplex method?

Pivoting involves making the pivot value 1 and the remaining entries in the pivot column 0. This is done to simplify and improve the solution with each iteration.

Summary & Key Takeaways

• Linear programming problems with more than two decision variables require the use of the simplex method for solution.

• The simplex method is an iterative process that starts with an initial feasible solution and improves it with each iteration.

• The steps of the simplex method include converting inequalities to equalities, creating the simplex tableau, determining the pivot column and row, pivoting, and checking for optimality.