ECON 3300 Exam #2

Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints. T/F

True

The shadow price for a positive decision variable is 0. T/F

True

The term continuous is synonymous with divisible in the context of linear programming. T/F

True

When using the graphical method, only one of the four quadrants of an xy-axis needs to be drawn.

True

extreme points

corner points on the boundary of the feasible solution area

Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once. T/F

false

feasible vs. infeasible

feasible= doesn't violate constraints infeasible= violates constraints

Multiple optimal solutions can occur when the objective function is ________ a constraint line.

parallel

Non-negativity constraints

restrict the decision variables to zero or positive values x1, x2 >= 0

marginal value

the dollar amount one would be willing to pay for one additional resource unit

unbounded problem

the objective function can increase indefinitely without reaching a maximum value. the solution area is not completely closed in.

sensitivity range

the range of values over which the current optimal solution point will remain optimal

proportionality

the slope of a constraint or objective function line is constant. Changes that happen in the decision variables, will happen in the functional value

sensitivity analysis

the use of linear programming to evaluate effects of changes in model parameters and how they affect optimal points

constraint lines are plotted as equations. T/F

true

graphical solutions are limited to linear programming with only two decision variables. T/F

true

the optimal solution in the linear programming model will always occur at the extreme points. T/F

true

In the absence of nonnegativity constraints, our solution cannot have zero values for decision variables. T/F

False

Proportionality means the slope of a constraint is proportional to the slope of the objective function. T/F

False

The equation 8xy = 32 satisfies the proportionality property of linear programming. T/F

False

The sensitivity range for a constraint quantity value is the range over which the optimal values of the decision variables do not change. T/F

False

The terms in the objective function or constraints are multiplicative. T/F

False

The first step in formulating a linear programming model is to define the objective function. T/F

False, it's first decision variables

The optimal solution for a graphical linear programming problem is the corner point that is the farthest from the origin. T/F

False, this is only true for maximization problem

When slack isn't equal to 0

Nonbinding

surplus variables

-excessive resources used -changing (>=) to (=) -subtracted from problem -contributes nothing objective function value

Slack variables

-unused resources -changing the (<=) to (=) -added to problem -contributes nothing objective function value

simplex method

A complicated mathematical method that helps solve linear programming problems.

When the slack is equal to 0

Binding

For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint: A) will have a positive value. B) will have a negative value. C) will have a value of zero. D) could have a positive, negative or a value of zero. (no sign restrictions).

C

For a resource constraint, either its slack value must be ________ or its shadow price must be ________. A) negative, negative B) negative, zero C) zero, zero D) zero, negative

C

shadow price

The change in the optimal objective function value per unit increase in the right-hand side of a constraint.

Sensitivity range for a right-hand-side value is

The range of values over which the quantity's value can change without changing the solution variable mix, including slack variables

The objective function is a linear relationship reflecting the objective of an operation. T/F

True

The sensitivity range for a constraint quantity value is the range over which the optimal values of the decision variable do not change. T/F

True

model constraints

a linear relationship that represents a restriction on decision making

linear programming

a model that consists of linear relationships representing a firm's decision(s), given an objective and resource constraints

Alternative optimal solutions

are the endpoints of the constraint line segment that the objective function parallels. all points represent the same optimal solution

objective function

linear relationship that reflects the objective of an operation

decision variables

mathematical symbols representing levels of activity of a firm

the optimal solution point is the last point/farthest to the objective function touches as it leaves the feasible solution area in a...

maximization problem

the optimal solution point is the closest to the origin in the feasible solution area in a...

minimization problem

parameters

numerical values that are included in the objective function and constraints