Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming

31) In a goal programming problem with two goals at the same priority level, all the deviational variables are equal to zero in the optimal solution. This means

A) there is no feasible solution to the problem.

B) all goals are fully achieved.

C) nonlinear programming must be used to solve this.

D) this problem was an integer programming problem.

E) None of the above

32) A goal programming problem had two goals (with no priorities assigned). Goal number 1 was to achieve a profit of $2,400 and goal number 2 was to have no idle time for workers in the factory. The optimal solution to this problem resulted in a profit of $2,300 and no idle time. What was the value for the objective function for this goal programming problem?

A) 2300

B) 100

C) -100

D) 0

E) None of the above

33) A goal programming problem had two goals (with no priorities assigned). Goal number 1 was to achieve a profit of $3,600 and goal number 2 was to have no wasted material. The optimal solution to this problem resulted in a profit of $3,300 and no wasted material. What was the value for the objective function for this goal programming problem?

A) 300

B) -300

C) 3300

D) 0

E) None of the above

34) In an integer programming problem, if it is desired to have variable X be exactly twice the value of variable Y, the constraint would be written

A) 2X + Y = 0.

B) X + 2Y = 0.

C) 2X - Y = 0.

D) X - 2Y = 0.

E) None of the above

Table 10-1

A company has decided to use 0-1 integer programming to help make some investment decisions. There are three possible investment alternatives from which to choose, but if it is decided that a particular alternative is to be selected, the entire cost of that alternative will be incurred (i.e., it is impossible to build one-half of a factory). The integer programming model is as follows:

Maximize 5000 X1 + 7000X2 + 9000X3

Subject to: X1 + X2 + X3 ? 2 (only 2 may be chosen)

25000X1 + 32000X2 + 29000X3 ? 62,000 (budget limit)

16 X1 + 14 X2 + 19 X3 ? 36 (resource limitation)

all variables = 0 or 1

where X1 = 1 if alternative 1 is selected, 0 otherwise

X2 = 1 if alternative 2 is selected, 0 otherwise

X3 = 1 if alternative 3 is selected, 0 otherwise

The optimal solution is X1 = 0, X2 = 1, X3 = 1

35) According to Table 10-1, which presents an integer programming problem, if the optimal solution is used, what would the value of the objective function be?

A) 21,000

B) 12,000

C) 16,000

D) 2

E) None of the above

36) According to Table 10-1, which presents an integer programming problem, if the optimal solution is used, how much of the budget would be spent?

A) $32,000

B) $29,000

C) $61,000

D) $62,000

E) None of the above

37) In Table 10-1, which presents an integer programming problem, using the optimal solution means only two of the alternatives would be selected. How much slack is there in the third constraint?

A) 0

B) 3

C) 33

D) 36

E) None of the above

38) According to Table 10-1, which presents an integer programming problem, the optimal solution is to select only two of the alternatives. Suppose you wished to add a constraint that stipulated that alternative 2 could only be selected if alternative 1 is also selected (i.e., if alternative 1 is not selected, you may not select alternative 2; however, you may select #1 and not select #2). How would this constraint be written?

A) X1 = X2

B) X1 ? X2

C) X1 ? X2

D) X1 + X2 = 2

E) None of the above

Table 10-2

Maximize Z = 34 X1 + 43 X2 + 29 X3

Subject to: 5 X1 + 4 X2 + 7 X3 ? 50

1 X1 + 2 X2 + 2 X3 ? 16

3 X1 + 4 X2 + 1 X3 ? 9

all Xi are integer and non-negative

Final Integer Solution: Z = 208

Decision

Variable Solution

X1 1

X2 0

X3 6

39) According to Table 10-2, which presents a solution for an integer programming problem, at the optimal solution, how much slack exists in the third constraint?

A) 0

B) 9

C) 5

D) 6

E) -1

40) We do not have a general method for solving all types of ________ problems.

A) mixed-integer programming

B) 0-1 integer programming

C) goal programming

D) nonlinear programming

E) pure integer programming

41) A capital budgeting problem involving the selection of possible projects under budget constraints is solved by which of the following?

A) mixed-integer programming

B) 0-1 integer programming

C) goal programming

D) nonlinear programming

E) pure integer programming

42) A transportation problem is an example of

A) a pure-integer programming problem.

B) a mixed-integer programming problem.

C) a zero-one integer programming problem.

D) a goal programming problem.

E) a nonlinear programming problem.

43) If we wish to develop a stock portfolio wherein we maximize return and minimize risk, we would have to use

A) pure-integer programming.

B) goal programming.

C) zero-one integer programming.

D) mixed-integer programming.

E) nonlinear programming.

44) Another name for a 0-1 variable is a(n) ________ variable.

A) either-or

B) binary

C) yes-no

D) quadratic

E) on-off

45) Terms that are minimized in goal programming are called

A) deviational variables.

B) global variables.

C) decision variables.

D) minimization variables.

E) None of the above

46) The concept of a local optimum is affiliated with which of the following?

A) mixed integer programming

B) integer programming

C) linear programming

D) nonlinear programming

E) goal programming

47) The concept of "satisficing" is affiliated with which of the following?

A) mixed integer programming

B) integer programming

C) linear programming

D) nonlinear programming

E) goal programming

48) The following

represents a:

A) goal programming problem.

B) mixed integer programming problem.

C) nonlinear programming problem.

D) 0-1 integer programming problem.

E) pure integer programming problem.

49) As part of a larger problem, you are trying to determine whether or not to open a plant with a capacity of 10,000 units (using binary variable Y). You also define X as the number of units (if any) produced at that plant. How will you ensure that Y will equal 1 if the plant is open?

A) Y ? X

B) Y ? X

C) X + Y ? 2

D) X = 10000Y

E) X ? 10000Y

50) Which of the following is not considered nonlinear programming?

A) nonlinear objective and nonlinear constraints

B) linear objective with nonlinear constraints

C) nonlinear objective with linear constraints

D) binary decision variable with nonlinear constraints

E) integer decision variable with linear constraints