The Simplex Method:
Definitions Page
- Objective Function
- The function that is either being minimized or maximized. For example, it may represent
the cost that you are trying to minimize.
- Optimal Solution
- A vector x which is both feasible (satisfying the constraints) and optimal
(obtaining the largest or smallest objective value).
- Constraints
- A set of equalities and inequalities that the feasible solution must satisfy.
- Feasible Solution
- A solution vector, x, which satisfies the constraints.
- Basic Solution
- x of (Ax=b) is a basic solution if the n components
of x can be partitioned into m "basic" and n-m
"non-basic" variables in such a way that:
- the m columns of A corresponding to the basic variables form a
nonsingular basis and
- the value of each "non-basic" variable is 0.
The constraint matrix A has m rows (constraints) and n
columns (variables).
- Basis
- The set of basic variables.
- Basic Variables
- A variable in the basic solution (value is not 0).
- Nonbasic Variables
- A variable not in the basic solution (value = 0).
- Slack Variable
- A variable added to the problem to eliminate less-than constraints.
- Surplus Variable
- A variable added to the problem to eliminate greater-than constraints.
- Artificial Variable
- A variable added to a linear program in phase 1 to aid finding a feasible solution.
- Unbounded Solution
- For some linear programs it is possible to make the objective arbitrarily small (without
bound). Such an LP is said to have an unbounded solution.
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