1. In problem formulation, the:
a. objective is expressed in terms of
the decision variables.
b. constraints are expressed in terms
of the obtained objective function
coefficients.
c. nonnegativity constraints are always
ignored.
d. optimal solution is decided upon.
2. A mathematical function in which each
variable appears in a separate term and
is raised to the first power is known as a
_____.
a. power function
b. linear function
c. what-if function
d. nonlinear function
variable appears in a separate term and
is raised to the first power is known as a
_____.
a. power function
b. linear function
c. what-if function
d. nonlinear function
3. A(n) _____ solution satisfies all the
constraint expressions simultaneously.
a. feasible
b. objective
c. infeasible
d. extreme
constraint expressions simultaneously.
a. feasible
b. objective
c. infeasible
d. extreme
4. The nonnegativity constraints create a
feasible region that is:
a. Unbound by the horizontal axis
only.
b. An area with no point satisfying all
the constraints.
c. Symmetric about the vertical axis
around the origin.
d. Bound by the horizontal and vertical
axes.
feasible region that is:
a. Unbound by the horizontal axis
only.
b. An area with no point satisfying all
the constraints.
c. Symmetric about the vertical axis
around the origin.
d. Bound by the horizontal and vertical
axes.
5. Geometrically, binding constraints
intersect to form the _____.
a. subspace
b. optimal point
c. decision cell
d. zero slack
intersect to form the _____.
a. subspace
b. optimal point
c. decision cell
d. zero slack
6. The _____ value for each less-than-orequal-to constraint indicates the
difference between the left-hand and
right-hand values for a constraint.
a. objective function coefficient
b. slack
c. unbounded
d. surplus
difference between the left-hand and
right-hand values for a constraint.
a. objective function coefficient
b. slack
c. unbounded
d. surplus
7. _____ is the situation in which no
solution to the linear programming
problem satisfies all the constraints.
a. Unboundedness
b. Divisibility 8. 9. 10. 11. 12. 13. c. Infeasibility
d. Optimality
The situation in which the value of the
solution may be made infinitely large in
a maximization linear programming
problem or infinitely small in a
minimization problem without violating
any of the constraints is known as
_____.
solution to the linear programming
problem satisfies all the constraints.
a. Unboundedness
b. Divisibility 8. 9. 10. 11. 12. 13. c. Infeasibility
d. Optimality
The situation in which the value of the
solution may be made infinitely large in
a maximization linear programming
problem or infinitely small in a
minimization problem without violating
any of the constraints is known as
_____.
a. infeasibility
b. unbounded
c. infiniteness
d. semi-optimality
The study of how changes in the input
parameters of a linear programming
problem affect the optimal solution is
known as_____.
b. unbounded
c. infiniteness
d. semi-optimality
The study of how changes in the input
parameters of a linear programming
problem affect the optimal solution is
known as_____.
a. regression analysis
b. cluster analysis
c. optimality analysis
d. sensitivity analysis
The change in the optimal objective
function value per unit increase in the
right-hand side of a constraint is given
by the _____.
a. objective function coefficient
b. shadow price
c. restrictive cost
d. right-hand side allowable increase
The imposition of integer restriction is
necessary for models where:
a. nonnegativity constraints are
needed.
b. variables can take negative values.
c. the decision variables cannot take
fractional values.
d. possible values of variables are
restricted to particular intervals.
The linear program that results from
dropping the integer requirements for
the variables in an integer linear
program is known as _____.
a. convex hull
b. a mixed-integer linear program
c. LP relaxation
d. a binary integer linear program
The objective function for an
optimization problem is: Max 5x – 3y,
with one of the constraints being x, y ?
0 and y integer. x and y are the only
decisions variables. This is an example
of a(n) _____. a. all-integer linear program
b. mixed-integer linear program
c. LP relaxation of the integer linear
program
d. binary integer linear program
b. cluster analysis
c. optimality analysis
d. sensitivity analysis
The change in the optimal objective
function value per unit increase in the
right-hand side of a constraint is given
by the _____.
a. objective function coefficient
b. shadow price
c. restrictive cost
d. right-hand side allowable increase
The imposition of integer restriction is
necessary for models where:
a. nonnegativity constraints are
needed.
b. variables can take negative values.
c. the decision variables cannot take
fractional values.
d. possible values of variables are
restricted to particular intervals.
The linear program that results from
dropping the integer requirements for
the variables in an integer linear
program is known as _____.
a. convex hull
b. a mixed-integer linear program
c. LP relaxation
d. a binary integer linear program
The objective function for an
optimization problem is: Max 5x – 3y,
with one of the constraints being x, y ?
0 and y integer. x and y are the only
decisions variables. This is an example
of a(n) _____. a. all-integer linear program
b. mixed-integer linear program
c. LP relaxation of the integer linear
program
d. binary integer linear program
14. Which of the following is true about the
sensitivity analysis for integer
optimization problems?
a. Sensitivity reports are readily
available for integer optimization
problems similar to the linear
programming problems.
b. Because of the discrete nature of
the integer optimization, Excel
Solver takes much more time to
calculate objective function
coefficient ranges, shadow prices,
and right-hand-side ranges.
c. The sensitivity analysis is not
important for integer problems.
d. To determine the sensitivity of the
solution to changes in model inputs
for integer optimization problems,
the data must be changed and the
problem must be re-solved.
sensitivity analysis for integer
optimization problems?
a. Sensitivity reports are readily
available for integer optimization
problems similar to the linear
programming problems.
b. Because of the discrete nature of
the integer optimization, Excel
Solver takes much more time to
calculate objective function
coefficient ranges, shadow prices,
and right-hand-side ranges.
c. The sensitivity analysis is not
important for integer problems.
d. To determine the sensitivity of the
solution to changes in model inputs
for integer optimization problems,
the data must be changed and the
problem must be re-solved.
15. The objective function for a linear
optimization problem is: Max 3x + 2y,
with one of the constraints being x, y =
0, 1. x and y are the only decision
variables. This is an example of a _____.
a. nonlinear program
b. mixed-integer linear program
c. LP relaxation of the integer linear
program
d. binary integer linear program
optimization problem is: Max 3x + 2y,
with one of the constraints being x, y =
0, 1. x and y are the only decision
variables. This is an example of a _____.
a. nonlinear program
b. mixed-integer linear program
c. LP relaxation of the integer linear
program
d. binary integer linear program
16. The _____ of a solution is a
mathematical concept that refers to the
set of points within a relatively close
proximity of the solution.
a. objective function contour
b. neighborhood
c. regression equation
d. Lagrangian multiplier
mathematical concept that refers to the
set of points within a relatively close
proximity of the solution.
a. objective function contour
b. neighborhood
c. regression equation
d. Lagrangian multiplier
17. A feasible solution is a(n) _____ if there
are no other feasible solutions with a
better objective function value in the
immediate neighborhood.
a. efficient frontier
b. local optimum
c. global maximum
d. diverging function
are no other feasible solutions with a
better objective function value in the
immediate neighborhood.
a. efficient frontier
b. local optimum
c. global maximum
d. diverging function
18. A feasible solution is _____ if there are
no other feasible points with a better
objective function value in the entire
feasible region.
a. infeasible
b. unbounded
c. nonlinear
d. a global optimum
no other feasible points with a better
objective function value in the entire
feasible region.
a. infeasible
b. unbounded
c. nonlinear
d. a global optimum
19. Reference – 10.3. Which of the following
equations is most likely to yield the
above curve?
a. f(X, Y) = Xlog(2?Y) + Ylog(2?X)
b. f(X, Y) = X – Y
c. f(X, Y) = –X2 – Y2
d. f(X, Y) = Xsin(5?X) + Ysin(5?Y)
equations is most likely to yield the
above curve?
a. f(X, Y) = Xlog(2?Y) + Ylog(2?X)
b. f(X, Y) = X – Y
c. f(X, Y) = –X2 – Y2
d. f(X, Y) = Xsin(5?X) + Ysin(5?Y)
20. The _____ option is helpful when the
solution to a problem appears to
depend on the starting values for the
decision variables.
a. Restart
b. Convergence
c. Derivatives
d. Multistart
solution to a problem appears to
depend on the starting values for the
decision variables.
a. Restart
b. Convergence
c. Derivatives
d. Multistart
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