Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming

1) If conditions require that all decision
variables must have an integer solution, then the class of problem described is
an integer programming problem.

2) An integer programming solution can
never produce a greater profit objective than the LP solution to the same
problem.

3) 0-1 integer programming might be
applicable to selecting the best gymnastics team to represent a country from
among all identified teams.

4) Nonlinear programming is the case in
which objectives and/or constraints are nonlinear.

5) The following objective function is
nonlinear: Max 5X + (1/8)Y – Z.

6) In goal programming, if all the goals
are achieved, then the value of the objective function will always be zero.

7) Unfortunately, multiple goals in goal
programming are not able to be prioritized and solved.

8) The following objective function is
nonlinear: Max 5X – 8YZ.

9) Goal programming permits multiple
objectives to be satisfied.
10) The constraint X1 + X2 ? 1 with
0 -1 integer programming allows for either X1 or X2 to be a
part of the optimal solution, but not both.

11) Requiring an integer solution to a
linear programming problem decreases the size of the feasible region.

12) The transportation problem is a good
example of a pure integer programming problem.

13) The three types of integer programs
are: pure integer programming, impure integer programming, and 0-1 integer
programming.

14) When solving very large integer
programming problems, we sometimes have to settle for a “good,” not
necessarily optimal, answer.

15) Quadratic programming contains squared
terms in the constraints.
16) In goal programming, our goal is to
drive the deviational variables in the objective function as close to zero as
possible.

17) There is no general method for solving
all nonlinear problems.

18) A 0-1 programming representation could
be used to assign sections of a course to specific classrooms.
19) In goal programming, the deviational
variables have the same objective function coefficients as the surplus and
slack variables in a normal linear program.
Answer:
FALSE
Diff: 2
Topic: GOAL PROGRAMMING
20) Unfortunately, goal programming, while
able to handle multiple objectives, is unable to prioritize these objectives.

21) A model containing a linear objective
function and linear constraints but requiring that one or more of the decision
variables take on an integer value in the final solution is called
A) a goal programming problem.
B) an integer programming problem.
C) a nonlinear programming problem.
D) a multiple objective LP problem.
E) a branch-and-bound programming problem.

22) Assignment problems solved previously
by linear programming techniques are also examples of
A) pure-integer programming problems.
B) mixed-integer programming problems.
C) zero-one integer programming problems.
D) goal programming problems.
E) nonlinear programming problems.

23) A mathematical programming model that
permits decision makers to set and prioritize multiple objective functions is
called a
A) pure-integer programming problem.
B) mixed-integer programming problem.
C) zero-one integer programming problem.
D) goal programming problem.
E) nonlinear programming problem.

24) Goal programming differs from linear
programming in which of the following aspects?
A) It tries to maximize deviations between
set goals and what can be achieved within the constraints.
B) It minimizes instead of maximizing as
in LP.
C) It permits multiple goals to be
combined into one objective function.
D) All of the above
E) None of the above
25) Which of the following is a category
of mathematical programming techniques that doesn’t assume linearity in the
objective function and/or constraints?
A) integer programs
B) goal programming problems
C) nonlinear programs
D) multiple objective programming problems
E) None of the above

26) A type of integer programming is
A) pure.
B) mixed.
C) zero-one.
D) All of the above
E) None of the above

27) Which of the following functions is
nonlinear?
A) 4X + 2Y + 7Z
B) -4X + 2Y
C) 4X + (1/2)Y + 7Z
D) Z
E) 4X/Y + 7Z

28) Goal programming is characterized by
A) all maximization problems.
B) setting of lower and upper bounds.
C) the deviation from a high-priority goal
must be minimized before the next-highest-priority goal may be considered.
D) All of the above
E) None of the above
9) An integer programming (maximization)
problem was first solved as a linear programming problem, and the objective
function value (profit) was $253.67. The two decision variables (X, Y) in the
problem had values of X = 12.45 and Y = 32.75. If there is a single optimal
solution, which of the following must be true for the optimal integer solution
to this problem?
A) X = 12 Y = 32
B) X = 12 Y = 33
C) The objective function value must be
less than $253.67.
D) The objective function value will be
greater than $253.67.
E) None of the above

30) An integer programming (minimization)
problem was first solved as a linear programming problem, and the objective
function value (cost) was $253.67. The two decision variables (X, Y) in the
problem had values of X = 12.45 and Y = 32.75. If there is a single optimal
solution, which of the following must be true for the optimal integer solution
to this problem?
A) X = 13 Y = 33
B) X = 12 Y = 32
C) The objective function value must be
less than $253.67.
D) The objective function value will be
greater than $253.67.

E)
None of the above