34 terms

Linear Programming Concepts

Econ 3300
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Which of the following is the most useful contribution of integer programming?
Using 0-1 variables for modeling flexibility
Sensitivity analysis information in computer output is based on the assumption of
one coefficient change
Media selection problems usually determine
How many times to use each media source
Rounded solutions to linear programs must be evaluated for
Feasibility and Optimality
A constraint with a positive slack value
will have a shadow price of zero
The maximization or minimization of a quantity is the
objective of linear programming
Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in
Standard form
The wrong ways to "find" the optimal solution to a linear programming problem using the graphical method
-find the feasible point that is the farthest away from the origin.
-find the feasible point that is at the highest location.
-find the feasible point that is closest to the origin.
The objective function for portfolio selection problems usually is maximization of expected return or
minimization of risk
The solution to the LP Relaxation of a maximization integer linear program provides
an upper bound for the value of the objective function
Rounding the solution of an LP Relaxation to the nearest integer values provides
an integer solution that might be neither feasible nor optimal.
Standard LP model
all the decision variables are of te nonnegative continuous (x ≥ 0) variety.
Integer LP model
at least one decision variable is of the nonnegative integer (x ≥ 0, integer) or binary (x = 1 or 0) variety.
Feasible solution
is a combination of values for the decision variables that satisfies all the constraints. The set of all feasible solutions is termed the feasible region.
Optimal Solution
A feasible solution for which no other feasible solution would yield a larger value for the objective function (in a maximization problem) or a smaller value for the objective function (in a minimization problem).
Every LP problem/model falls into one of the following four mutually exclusive categories
Exactly one optimal solution, Multiple optimal solutions, infeasible problem, unbounded problem
satisfying a ≥ constraint, the constraint will have a (0 or positive) surplus defined as
LHS - RHS
satisfying a ≤ constraint, the constraint will have a (0 or positive) slack, defined as
RHS -LHS
satisfying an = constraint, LHS = RHS
the constraint has a slack or surplus = 0
A constraint whose slack or surplus = 0 at that optimal solution (i.e., with LHS = RHS at the optimal solution) is called
a binding constraint
A constraint whose slack or surplus is > 0 at that optimal solution is called
a non-binding constraint
If, making no other changes, one constraint's RHS is increased by any positive amount A up to its allowable increase, then:
the optimal value of the objective function will increase by A•(shadow price); and a change in the optimal value will be accompanied by a change in the optimal solution
If, making no other changes, one constraint's RHS is decreased by any positive amount A up to its allowable decrease, then:
the optimal value of the objective function will decrease by A•(shadow price); and a change in the optimal value will be accompanied by a change in the optimal solution
Range of feasibility
the range of values over which the dual price is applicable.
__ _____ constraint will always have a shadow price of 0
A non-binding
__ _____ constraint can have a positive, negative, or 0 shadow price
A binding
Decision Variables
Tell how much or how many of something to produce, invest, purchase, hire, etc.
Infeasible solution
Satisfies all the constraints of a linear programming problem except the nonnegativity constraints
Slack
is the amount by which the left side of a ≤ constraint is smaller than the right side.
Shadow Price
The changes the value of the objective function per unit increase in a right-hand side
As long as the slope of the objective function stays between the slopes of the binding constraints
the optimal solution won't change
Infeasibility
means that the number of solutions to the linear programming models that satisfies all constraints is 0
A range of optimality
is applicable only if the other coefficient remains at the original value
An optimal solution to a linear programming problem can be found
at an extreme point of the feasible region for the problem
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