Basic Terms Involved in Simplex Method-
1. Standard Form of an L.P.P. : In standard form of the objective function, namely, maximize or minimize, all the constraints are expressed as equations moreover R.H.S. of each constraint and all variables are non-negative.
2. Slack Variables: These variables are added to less than or equal to type constraints to change it into equality.
3. Surplus Variables: These variables are substrates from a greater than or equal to type constraint to change it into equality.
4. Basic Solution: Given a system of m linear equations with n variables (m < n). Any solution which is obtained by solving for m variables keeping the remaining (n–m) variables zero is called a basic solution.
5. Basic Feasible Solution: A basic solution, which also satisfies the non-negative constraints, is called basic feasible solution.
6. Non-Degenerate Basic Solution: It is the basic feasible solution, which has exactly m positive, i.e., none of basic variables are zero.
7. Degenerate Basic Feasible Solution: A B.F.S. is said to be degenerate if one or more basic variables are zero.
8. Feasible Solution: Any solution to an L.P.P. which satisfies the non-negative restrictions, is called feasible solution.
9. Optimal Solution: A basic feasible solution of an L.P.P. which gives optimum value of the objective function is called optimal solution.
10. Unbounded Solution: If the value of the objective function Z can be increased or decreased indefinitely, such solutions are called unbounded solutions.
11. Canonical Form: In canonical form, if the objective function is of maximization, all the constraints other than non-negative conditions are ≤ type. If the objective function is of minimization, all the constraints other than non-negative conditions are ≥ type.
