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
