Optimization Exam 1 Flashcards
Any specification of the decision variables that satisfies all of the model’s constraints.
Feasible Region
The amounts of things that will minimize or maximize something.
Decision Variables
Any point in the feasible region.
Feasible Point
Any point in the feasible region that optimizes the objective function.
Optimal Solution
The objective function evaluated at the optimal solution.
Optimal Value
A line on which all points have the same z-value in a max problem.
Isoprofit Line
A line on which all points have the same z-value in a min problem.
Isocost Line
If the left hand side and right hand side of the constraint are equal when the optimal values of the decision variables are substituted into the constraint.
Binding Constraint
If the left hand side and right hand side of the constraint are unequal when the optimal values of the decision variables are substituted into the constraint.
Nonbinding Constraint
For a set of points S, if the line segment joining any pair of points is wholly contained in S.
Convex Set
If each line segment that lies completely in a convex set S and contains the point P has a P as an endpoint of the line segment.
Extreme Point
The feasible region of a problem contains points for which the value of at least one variable can assume arbitrary large values.
Unbounded Feasible Region
No possible point that satisfies the constraints.
Infeasible LP
Transforms a given matrix A into a new matrix A’.
Elementary Row Operation (ERO)
An algorithm that can be used to solve systems of linear equations.
Gauss-Jordan Elimination
A variable that appears with a coefficient of 1 in a single equation and a coefficient of 0 in all other equations.
Basic Variable
Any variable that isn’t a basic variable.
Nonbasic Variable
An LP that has a maximum objective, non-negative right hand side, only equality constraints, and non-negative decision variables.
Standard Form LP
Picks up slack for inequalities.
Slack Variable
Any basic solution to the system Ax=b in which all variables are non-negative.
Basic Feasible Solution (BFS)
A point in the feasible region of an LP is an extreme point if and only if it is a basic feasible solution to the LP.
Theorem 1
If two basic solutions and their sets of basic variables have m-1 basic variables in common. m = number of constraints.
Adjacent Basic Variables
