Solution Manual: Optimization in Operations Research 2nd
Edition by Rardin - Ch. 1-17, 9780134384559, with Rationales
A nonlinear optimization problem is any optimization problem in which at least one term in the
objective function or a constraint is nonlinear. - ANSWER: True
A function is quadratic if its nonlinear terms have a power of 4. - ANSWER: False
Nonlinear programming algorithms are more complex than linear programming algorithms. -
ANSWER: True
Many linear programming algorithms such as the simplex method optimize by examining only the
extreme points - ANSWER: True
Nonlinear optimization problems can have only one local optimal solution. - ANSWER: False
A feasible solution is a global optimum if there are no other feasible solutions with a better objective
fun - ANSWER: False
A feasible solution is a global optimum if there are no other feasible points with a better objective
function value in the feasible region. - ANSWER: True
For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand
side values. - ANSWER: False
The interpretation of the dual price for nonlinear models is different than the interpretation of the
dual price for linear models. - ANSWER: False
In the case of functions with multiple local optima, most nonlinear optimization software methods
can get stuck and terminate at a local optimum. - ANSWER: True
For a minimization problem, a point is a global minimum if there are no other feasible points with a
smaller objective function value. - ANSWER: True
There are nonlinear applications in which there is a single local optimal solution that is also the global
optimal solution. - ANSWER: True
Functions that are convex have a single local maximum that is also the global maximum. - ANSWER:
False
The function f (X, Y) = X 2 + Y 2 has a single global minimum and is relatively easy to minimize. -
ANSWER: True
The problem of maximizing a concave quadratic function over a linear constraint set is relatively
difficult to solve. - ANSWER: False
Each point on the efficient frontier is the maximum possible risk, measured by portfolio variance, for
the given return. - ANSWER: False
Any feasible solution to a blending problem with pooled components is feasible to the problem with
no pooling. - ANSWER: True
Any feasible solution to a blending problem without pooled components is feasible to the problem
with pooled components. - ANSWER: False
,When components (or ingredients) in a blending problem must be pooled, the number of feasible
solutions is reduced. - ANSWER: True
The value of the coefficient of imitation, q, in the Bass model for forecasting adoption of a new
product cannot be negative. - ANSWER: False
The Markowitz mean-variance portfolio model presented in the text is a convex optimization
problem. - ANSWER: True
Because most nonlinear optimization codes will terminate with a local optimum, the solution
returned by the codes will be the best solution. - ANSWER: False
It is possible for the optimal solution to a nonlinear optimization problem to lie in the interior of the
feasible region. - ANSWER: True
Which of the following is incorrect?
a. A global optimum is a local optimum in a nonlinear optimization problem.
b. A local maximum is a global maximum in a concave nonlinear optimization problem.
c. A global minimum is a local minimum in a convex nonlinear optimization problem.
d. A local optimum is a global optimum in a nonlinear optimization problem. - ANSWER: d. A local
optimum is a global optimum in a nonlinear optimization problem.
The measure of risk most often associated with the Markowitz portfolio model is the
a. portfolio average return.
b. portfolio minimum return.
c. portfolio variance.
d. portfolio standard deviation. - ANSWER: c. portfolio variance.
An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at
a graph of the
a. feasible region.
b. pooled components.
c. rolling horizon.
d. efficient frontier. - ANSWER: d. efficient frontier.
Which of the following is not a parameter of the Bass model for forecasting adoption of a new
product?
a. the coefficient of innovation
b. the coefficient of interaction
c. the coefficient of imitation
d. the estimated number of people to eventually adopt the new product - ANSWER: b. the coefficient
of interaction
When the number of blending components exceeds the number of storage facilities, the number of
feasible solutions to the blending problem
a. is reduced.
b. is increased.
c. is unchanged.
d. is zero. - ANSWER: a. is reduced.
In the Bass model for forecasting the adoption of a new product, the objective function
a. minimizes the sum of forecast errors.
b. minimizes the sum of squared forecast errors.
c. maximizes the number of adoptions.
d. maximizes the number of adoptions and imitations. - ANSWER: b. minimizes the sum of squared
forecast errors.
,Which of the following is not true regarding a concave function?
a. It is bowl-shaped down.
b. It is relatively easy to maximize.
c. It has multiple local maxima.
d. It has a single global maximum. - ANSWER: c. It has multiple local maxima.
A convex function is
a. bowl-shaped up.
b. bowl-shaped down.
c. elliptical in shape.
d. sinusoidal in shape. - ANSWER: a. bowl-shaped up.
If the coefficient of each squared term in a quadratic function is positive, the function is
a. concave.
b. convex.
c. elliptical.
d. sinusoidal. - ANSWER: b. convex.
Components that share a storage facility are called
a. constrained components.
b. indexed components.
c. blended components.
d. pooled components. - ANSWER: d. pooled components.
The key idea behind constructing an index fund is to choose a portfolio of securities that
a. is a mix of growth-oriented and income-oriented stocks.
b. minimizes risk without sacrificing liquidity.
c. mimics the performance of a broad market index.
d. balances short-term and long-term investments. - ANSWER: c. mimics the performance of a broad
market index.
Components are referred to as pooled if they
a. are shared by two or more customers b. have common ingredients
c. share a storage facility d. are interchangeable - ANSWER: c. share a storage facility
Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal
solution. - ANSWER: False
In a linear programming problem, the objective function and the constraints must be linear functions
of the decision variables. - ANSWER: True
In a feasible problem, an equal-to constraint cannot be nonbinding. - ANSWER: True
Only binding constraints form the shape (boundaries) of the feasible region. - ANSWER: False
The constraint 5x1 − 2x2 ≤ 0 passes through the point (20, 50). - ANSWER: True
A redundant constraint is a binding constraint. - ANSWER: False
Because surplus variables represent the amount by which the solution exceeds a minimum target,
they are given positive coefficients in the objective function. - ANSWER: False
Alternative optimal solutions occur when there is no feasible solution to the problem. - ANSWER:
False
A range of optimality is applicable only if the other coefficient remains at its original value. - ANSWER:
True
, Because the dual price represents the improvement in the value of the optimal solution per unit
increase in right-hand-side, a dual price cannot be negative. - ANSWER: False
Decision variables limit the degree to which the objective in a linear programming problem is
satisfied. - ANSWER: False
No matter what value it has, each objective function line is parallel to every other objective function
line in a problem. - ANSWER: True
The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30. - ANSWER: True
The constraint 2x1 − x2 = 0 passes through the point (200,100). - ANSWER: False
The standard form of a linear programming problem will have the same solution as the original
problem. - ANSWER: True
An optimal solution to a linear programming problem can be found at an extreme point of the
feasible region for the problem. - ANSWER: True
An unbounded feasible region might not result in an unbounded solution for a minimization or
maximization problem. - ANSWER: True
An infeasible problem is one in which the objective function can be increased to infinity. - ANSWER:
False
A linear programming problem can be both unbounded and infeasible. - ANSWER: False
It is possible to have exactly two optimal solutions to a linear programming problem. - ANSWER: False
The maximization or minimization of a quantity is the
a. goal of management science.
b. decision for decision analysis.
c. constraint of operations research.
d. objective of linear programming. - ANSWER: d. objective of linear programming.
22. Decision variables
a. tell how much or how many of something to produce, invest, purchase, hire, etc.
b. represent the values of the constraints.
c. measure the objective function.
d. must exist for each constraint. - ANSWER: a. tell how much or how many of something to produce,
invest, purchase, hire, etc.
23. Which of the following is a valid objective function for a linear programming problem?
a. Max 5xy
b. Min 4x + 3y + (2/3)z
c. Max 5x2 + 6y2
d. Min (x1 + x2)/x3 - ANSWER: b. Min 4x + 3y + (2/3)z
24. Which of the following statements is NOT true?
a. A feasible solution satisfies all constraints.
b. An optimal solution satisfies all constraints.
c. An infeasible solution violates all constraints.
d. A feasible solution point does not have to lie on the boundary of the feasible region. - ANSWER: c.
An infeasible solution violates all constraints
Edition by Rardin - Ch. 1-17, 9780134384559, with Rationales
A nonlinear optimization problem is any optimization problem in which at least one term in the
objective function or a constraint is nonlinear. - ANSWER: True
A function is quadratic if its nonlinear terms have a power of 4. - ANSWER: False
Nonlinear programming algorithms are more complex than linear programming algorithms. -
ANSWER: True
Many linear programming algorithms such as the simplex method optimize by examining only the
extreme points - ANSWER: True
Nonlinear optimization problems can have only one local optimal solution. - ANSWER: False
A feasible solution is a global optimum if there are no other feasible solutions with a better objective
fun - ANSWER: False
A feasible solution is a global optimum if there are no other feasible points with a better objective
function value in the feasible region. - ANSWER: True
For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand
side values. - ANSWER: False
The interpretation of the dual price for nonlinear models is different than the interpretation of the
dual price for linear models. - ANSWER: False
In the case of functions with multiple local optima, most nonlinear optimization software methods
can get stuck and terminate at a local optimum. - ANSWER: True
For a minimization problem, a point is a global minimum if there are no other feasible points with a
smaller objective function value. - ANSWER: True
There are nonlinear applications in which there is a single local optimal solution that is also the global
optimal solution. - ANSWER: True
Functions that are convex have a single local maximum that is also the global maximum. - ANSWER:
False
The function f (X, Y) = X 2 + Y 2 has a single global minimum and is relatively easy to minimize. -
ANSWER: True
The problem of maximizing a concave quadratic function over a linear constraint set is relatively
difficult to solve. - ANSWER: False
Each point on the efficient frontier is the maximum possible risk, measured by portfolio variance, for
the given return. - ANSWER: False
Any feasible solution to a blending problem with pooled components is feasible to the problem with
no pooling. - ANSWER: True
Any feasible solution to a blending problem without pooled components is feasible to the problem
with pooled components. - ANSWER: False
,When components (or ingredients) in a blending problem must be pooled, the number of feasible
solutions is reduced. - ANSWER: True
The value of the coefficient of imitation, q, in the Bass model for forecasting adoption of a new
product cannot be negative. - ANSWER: False
The Markowitz mean-variance portfolio model presented in the text is a convex optimization
problem. - ANSWER: True
Because most nonlinear optimization codes will terminate with a local optimum, the solution
returned by the codes will be the best solution. - ANSWER: False
It is possible for the optimal solution to a nonlinear optimization problem to lie in the interior of the
feasible region. - ANSWER: True
Which of the following is incorrect?
a. A global optimum is a local optimum in a nonlinear optimization problem.
b. A local maximum is a global maximum in a concave nonlinear optimization problem.
c. A global minimum is a local minimum in a convex nonlinear optimization problem.
d. A local optimum is a global optimum in a nonlinear optimization problem. - ANSWER: d. A local
optimum is a global optimum in a nonlinear optimization problem.
The measure of risk most often associated with the Markowitz portfolio model is the
a. portfolio average return.
b. portfolio minimum return.
c. portfolio variance.
d. portfolio standard deviation. - ANSWER: c. portfolio variance.
An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at
a graph of the
a. feasible region.
b. pooled components.
c. rolling horizon.
d. efficient frontier. - ANSWER: d. efficient frontier.
Which of the following is not a parameter of the Bass model for forecasting adoption of a new
product?
a. the coefficient of innovation
b. the coefficient of interaction
c. the coefficient of imitation
d. the estimated number of people to eventually adopt the new product - ANSWER: b. the coefficient
of interaction
When the number of blending components exceeds the number of storage facilities, the number of
feasible solutions to the blending problem
a. is reduced.
b. is increased.
c. is unchanged.
d. is zero. - ANSWER: a. is reduced.
In the Bass model for forecasting the adoption of a new product, the objective function
a. minimizes the sum of forecast errors.
b. minimizes the sum of squared forecast errors.
c. maximizes the number of adoptions.
d. maximizes the number of adoptions and imitations. - ANSWER: b. minimizes the sum of squared
forecast errors.
,Which of the following is not true regarding a concave function?
a. It is bowl-shaped down.
b. It is relatively easy to maximize.
c. It has multiple local maxima.
d. It has a single global maximum. - ANSWER: c. It has multiple local maxima.
A convex function is
a. bowl-shaped up.
b. bowl-shaped down.
c. elliptical in shape.
d. sinusoidal in shape. - ANSWER: a. bowl-shaped up.
If the coefficient of each squared term in a quadratic function is positive, the function is
a. concave.
b. convex.
c. elliptical.
d. sinusoidal. - ANSWER: b. convex.
Components that share a storage facility are called
a. constrained components.
b. indexed components.
c. blended components.
d. pooled components. - ANSWER: d. pooled components.
The key idea behind constructing an index fund is to choose a portfolio of securities that
a. is a mix of growth-oriented and income-oriented stocks.
b. minimizes risk without sacrificing liquidity.
c. mimics the performance of a broad market index.
d. balances short-term and long-term investments. - ANSWER: c. mimics the performance of a broad
market index.
Components are referred to as pooled if they
a. are shared by two or more customers b. have common ingredients
c. share a storage facility d. are interchangeable - ANSWER: c. share a storage facility
Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal
solution. - ANSWER: False
In a linear programming problem, the objective function and the constraints must be linear functions
of the decision variables. - ANSWER: True
In a feasible problem, an equal-to constraint cannot be nonbinding. - ANSWER: True
Only binding constraints form the shape (boundaries) of the feasible region. - ANSWER: False
The constraint 5x1 − 2x2 ≤ 0 passes through the point (20, 50). - ANSWER: True
A redundant constraint is a binding constraint. - ANSWER: False
Because surplus variables represent the amount by which the solution exceeds a minimum target,
they are given positive coefficients in the objective function. - ANSWER: False
Alternative optimal solutions occur when there is no feasible solution to the problem. - ANSWER:
False
A range of optimality is applicable only if the other coefficient remains at its original value. - ANSWER:
True
, Because the dual price represents the improvement in the value of the optimal solution per unit
increase in right-hand-side, a dual price cannot be negative. - ANSWER: False
Decision variables limit the degree to which the objective in a linear programming problem is
satisfied. - ANSWER: False
No matter what value it has, each objective function line is parallel to every other objective function
line in a problem. - ANSWER: True
The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30. - ANSWER: True
The constraint 2x1 − x2 = 0 passes through the point (200,100). - ANSWER: False
The standard form of a linear programming problem will have the same solution as the original
problem. - ANSWER: True
An optimal solution to a linear programming problem can be found at an extreme point of the
feasible region for the problem. - ANSWER: True
An unbounded feasible region might not result in an unbounded solution for a minimization or
maximization problem. - ANSWER: True
An infeasible problem is one in which the objective function can be increased to infinity. - ANSWER:
False
A linear programming problem can be both unbounded and infeasible. - ANSWER: False
It is possible to have exactly two optimal solutions to a linear programming problem. - ANSWER: False
The maximization or minimization of a quantity is the
a. goal of management science.
b. decision for decision analysis.
c. constraint of operations research.
d. objective of linear programming. - ANSWER: d. objective of linear programming.
22. Decision variables
a. tell how much or how many of something to produce, invest, purchase, hire, etc.
b. represent the values of the constraints.
c. measure the objective function.
d. must exist for each constraint. - ANSWER: a. tell how much or how many of something to produce,
invest, purchase, hire, etc.
23. Which of the following is a valid objective function for a linear programming problem?
a. Max 5xy
b. Min 4x + 3y + (2/3)z
c. Max 5x2 + 6y2
d. Min (x1 + x2)/x3 - ANSWER: b. Min 4x + 3y + (2/3)z
24. Which of the following statements is NOT true?
a. A feasible solution satisfies all constraints.
b. An optimal solution satisfies all constraints.
c. An infeasible solution violates all constraints.
d. A feasible solution point does not have to lie on the boundary of the feasible region. - ANSWER: c.
An infeasible solution violates all constraints
