Linear Programming Flashcards
What is Linear Programming?
A technique for optimization of a linear objective function, subject to linear equality and inequality constraints.
What is the graphical method of solving LP?
A way to visualize the feasible region and find the optimal solution by graphing the constraints and objective function. Effective mainly for problems with two decision variables.
What defines a feasible solution in LP?
A solution that satisfies all constraints of the LP.
How do you identify the optimal solution using the graphical method?
By finding the point on the feasible region boundary where the objective function reaches its maximum or minimum value.
What is the Simplex method?
A popular algorithm for solving linear programming problems that transforms the constraints into a tableau and iteratively adjusts to find the optimal solution.
What is a tableau in the context of the Simplex method?
A tabular representation of an LP problem used in the Simplex method to perform calculations more systematically.
How is the optimal solution found using the Simplex method?
By performing pivot operations on the tableau until no negative numbers remain in the bottom row, indicating that the maximum or minimum value has been reached.
What are artificial variables in the context of the Simplex method?
Variables added to the LP to transform inequalities into equations to find a starting feasible solution.
What is the purpose of the Two-Phase method in the Simplex algorithm?
To find a feasible starting point in Phase 1 using artificial variables and then solve the original LP problem in Phase 2.
How does the Two-Phase method work?
Phase 1 adds artificial variables to find a feasible solution. If successful, Phase 2 starts with this solution and solves the original problem without the artificial variables.
