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.

-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