Question 1

A linear programming problem with _____decision variable(s)can be solved by a graphical solution method.
A)two
B)three
C)four
D)five

Accepted Answer

A graphical solution method is practical and feasible for linear programming problems with two decision variables because it allows for the visualization of constraints and the objective function on a two-dimensional graph.

Question 2

The prototype linear programming problem is to select an optimal mix of products to produce to maximize profit.This type of problem is referred to as the _____ problem.
A)product mix
B)production
C)product/process
D)product scheduling

Accepted Answer

The prototype linear programming problem described is specifically referred to as the "product mix" problem, where the goal is to determine the optimal combination of products to produce in order to maximize profit.

Question 3

A feasible solution is a solution that satisfies all of the constraints.

Accepted Answer

A feasible solution is indeed one that meets all the constraints of the problem, fitting within the defined parameters or limitations.

Question 4

The value to be optimized in an optimization model (such as profit)is called the objective.

Accepted Answer

In an optimization model, the value that is being maximized or minimized (such as profit) is indeed referred to as the objective or objective function.

Question 5

Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y.An algebraic formulation of these constraints is
A)  .
B)  .
C)  .
D)  .

Accepted Answer

The answer of Suppose a firm must at least meet...

Question 6

Suppose a company sells two different products,x and y,for net profits of $5 per unit and $10 per unit,respectively.The slope of the line representing the objective function is
A)0.5.
B)-0.5.
C)2.
D)-2.

Accepted Answer

The slope of the objective function, which represents the relationship between the profits from products x and y, is calculated as the ratio of the profits per unit of y to x. Thus, the slope = $10/$5 = 2. However, since the slope is typically represented as y over x (rise over run), and in this context, it represents a trade-off or exchange rate between the two products, the correct interpretation should reflect the decrease in x for an increase in y, hence -0.5.

Question 7

As related to sensitivity analysis in linear programming,when the profit increases with a unit increase in labor,this change in profit is referred to as the
A)add-in price.
B)sensitivity price.
C)shadow price.
D)additional profit.

Accepted Answer

The shadow price in linear programming refers to the change in the objective function value (e.g., total profit) for a one-unit increase in the right-hand side of a constraint (e.g., labor). It indicates the value of an additional unit of a resource.

Question 8

In most cases,when solving linear programming problems,we want the decision variables to be
A)equal to zero.
B)nonnegative.
C)nonpositive.
D)continuous.

Accepted Answer

Linear programming problems typically require decision variables to be nonnegative, meaning they cannot be less than zero. This is because these variables often represent quantities that cannot be negative, such as the amount of resources used or products produced.

Question 9

The optimal solution to any linear programming model is the
A)maximum objective function line.
B)minimum objective function line.
C)corner point of a polygon.
D)maximum or minimum of a parabola.

Accepted Answer

The optimal solution to a linear programming problem is found at the corner point(s) of the feasible region, which is often a polygon in two-dimensional space. This is due to the linear nature of both the objective function and the constraints in linear programming.

Question 10

Every linear programming problem involves optimizing a
A)linear regression model subject to several linear constraints.
B)linear function subject to several linear constraints.
C)linear function subject to several non-linear constraints.
D)non-linear function subject to several linear constraints.

Accepted Answer

Linear programming involves optimizing a linear function subject to several linear constraints, not non-linear constraints or functions, nor does it involve linear regression models.

Question 11

When using the graphical solution method to solve linear programming problems,the set of points that satisfy all constraints is called the _____ region.
A)optimal
B)feasible
C)constrained
D)logical

Accepted Answer

The set of points that satisfy all constraints in a linear programming problem is known as the feasible region. This region represents all possible solutions that meet the problem's requirements.

Question 12

The most important solution method for linear programming problems is known as the _____ method.
A)spreadsheet
B)solution mix
C)complex
D)simplex

Accepted Answer

The simplex method is the most important and widely used solution method for solving linear programming problems.

Question 13

An efficient algorithm for finding the optimal solution in a linear programming model is the _____ method.
A)spreadsheet
B)solution mix
C)complex
D)simplex

Accepted Answer

The simplex method is an efficient algorithm used for finding the optimal solution in a linear programming model.

Question 14

What is the equation of the line representing this constraint? 
A) 
B) 
C) 
D)

Accepted Answer

The answer of What is the equation of the line...

Question 15

The feasible region in all linear programming problems is bounded by
A)corner points.
B)hyperplanes.
C)an objective line.
D)all of these options.

Accepted Answer

The feasible region in linear programming problems is bounded by hyperplanes, which are geometric representations of the constraints in the problem. These hyperplanes are essentially the lines (in two dimensions), planes (in three dimensions), or higher-dimensional analogs that define the limits of the feasible region. Corner points and an objective line are elements related to the feasible region and the optimization process, but they do not bound the feasible region themselves.

Question 16

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is
A)  .
B)  .
C)  .
D)  .

Accepted Answer

The answer of If a manufacturing process takes 3 hours...

Question 17

In an optimization model,there can only be one
A)decision variable.
B)constraint.
C)objective function.
D)shadow price.

Accepted Answer

In an optimization model, there is typically only one objective function, which defines the goal of the optimization, such as maximizing profit or minimizing cost. Decision variables, constraints, and shadow prices can all have multiple instances within a single model.

Question 18

All optimization problems have
A)an objective function and decision variables.
B)an objective function and constraints.
C)decision variables and constraints.
D)an objective function,decision variables and constraints.

Accepted Answer

The answer of All optimization problems have
A)an objective function and...

Question 19

The term nonnegativity refers to the condition in which the
A)objective function cannot be less than zero.
B)decision variables cannot be less than zero.
C)right hand side of the constraints cannot be greater than zero.
D)reduced cost cannot be less than zero.

Accepted Answer

Nonnegativity is a condition applied to decision variables in optimization problems, indicating that these variables cannot take on negative values. This is a common requirement in many practical optimization problems where negative values do not make sense, such as quantities of products to produce or hours to work.

Question 20

Linear programming is a subset of a larger class of models called _____ models.
A)mathematical programming
B)mathematical optimality
C)linear regression
D)linear simplex

Accepted Answer

Linear programming is a specific type of mathematical programming, which is a broader class of models used for optimizing a linear objective function, subject to linear equality and linear inequality constraints.

Quiz 13: Introduction to Optimization Modeling

A linear programming problem with _____decision variable(s) can be solved by a graphical solution method.

The prototype linear programming problem is to select an optimal mix of products to produce to maximize profit.This type of problem is referred to as the _____ problem.

A feasible solution is a solution that satisfies all of the constraints.

The value to be optimized in an optimization model (such as profit)is called the objective.

Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y.An algebraic formulation of these constraints is

Suppose a company sells two different products,x and y,for net profits of $5 per unit and $10 per unit,respectively.The slope of the line representing the objective function is

As related to sensitivity analysis in linear programming,when the profit increases with a unit increase in labor,this change in profit is referred to as the

In most cases,when solving linear programming problems,we want the decision variables to be

The optimal solution to any linear programming model is the

Every linear programming problem involves optimizing a

When using the graphical solution method to solve linear programming problems,the set of points that satisfy all constraints is called the _____ region.

The most important solution method for linear programming problems is known as the _____ method.

An efficient algorithm for finding the optimal solution in a linear programming model is the _____ method.

What is the equation of the line representing this constraint?

The feasible region in all linear programming problems is bounded by

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is

In an optimization model,there can only be one

All optimization problems have

The term nonnegativity refers to the condition in which the

Linear programming is a subset of a larger class of models called _____ models.