A quadratic programming problem involves which of the following conditions?
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51) A quadratic programming problem
involves which of the following conditions?
A) squared terms in the objective function
and linear constraints
B) linear objective function and squared
terms in the constraints
C) squared terms in both the objective
function and constraints
D) a strictly goal programming problem
with squared terms in the objective function
E) None of the above
52) Which of the following statements is false
concerning goal programming?
A) The objective function is the main
difference between linear programming and goal programming.
B) The objective in goal programming is to
minimize deviational variables.
C) Deviational variables are zero if a
goal is completely obtained.
D) It is not possible for two goals to
have equal priority.
E) The priorities of each goal are
reflected in the objective function.
53) Consider the following 0-1 integer
programming problem:
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If we wish to add the constraint that no
more than two of these variables must be positive, how would this be written?
A) 2X + 2Y + 2Z ? 3
B) X + Y + Z ? 2
C) X ? 2, and Y ? 2, and Z ? 2
D) X, Y, Z ? 2
E) None of the above
54) Consider the following 0 – 1 integer
programming problem:
.jpg”>
If we wish to add the constraint that X
must be positive, and that only Y or Z, but not both, can be positive, how
would the additional constraint(s) be written?
A) X + Y + Z ? 3, Y + Z ? 1
B) X ? 1, Y + Z = 1
C) X ? 2, and Y ? 2, and Z ? 2
D) X = 1, Y + Z ? 1
E) None of the above
55) 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. 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) X = 12
D) Y = 32
E) None of the above
56) The overall best solution in a
nonlinear program is a
A) global optimum.
B) local optimum.
C) binary optimum.
D) nonlinear optimum.
E) goal optimum.
57) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a cost 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 cost of $2,400 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
58) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a cost of
$3,600 and goal number 2 was to have no wasted material. The optimal solution
to this problem resulted in a cost of $3,900 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
Table 10-3
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 Constraint
1
-X1 + X2 ? 0 Constraint
2
25,000 X1 + 32,000 X2 + 29,000 X3 ? 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
Solution x1 = 1, x2 = 0, x3 = 1, objective value = 14,000.
59) Table 10-3 presents an integer
programming problem. What is the meaning of Constraint 1?
A) If X1 is selected, X2 must also be selected.
B) No more than two alternatives may be
selected.
C) At least two alternatives must be
selected.
D) If X2 is selected, X1 must also be selected.
E) None of the above
60) Table 10-3 presents an integer
programming problem. What is the meaning of Constraint 2?
A) Both alternatives 1 and 2 must be
selected.
B) If alternative 2 is selected,
alternative 1 must also be selected.
C) Either alternative 1 or alternative 2
must be selected.
D) No more than one alternative may be
selected.
E) None of the above
61) Table 10-3 presents an integer
programming problem. If the optimal solution is used, then only two of the
alternatives would be selected. How much slack would there be in the third
constraint?
A) 1000
B) 5000
C) 3300
D) 8000
E) None of the above
62) Table 10-3 presents an integer
programming problem. Suppose you wish to add a constraint that stipulates that
both alternative 2 and alternative 3 must be selected, or neither can be
selected. How would this constraint be written?
A) X2 = X3
B) X2 ? X3
C) X2 ? X3
D) X2 + X3 = 1
E) None of the above
Table 10-4
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63) Table 10-4 represents a solution to a
goal programming problem. There are three goals (each represented by a
constraint). Which goals are only partly achieved?
A) number 1 only
B) number 1 and number 2
C) number 2 and number 3
D) number 1 and number 3
E) None of the above
64) Table 10-4 represents a solution to a
goal programming problem. There are three goals (each represented by a
constraint). Goal number 3 represents a resource usage goal. How much of this
resource would be used by this solution?
A) 50 units
B) 70 units
C) 2500 units
D) 240 units
E) None of the above
65) Table 10-4 represents a solution to a
goal programming problem. There are three goals (each represented by a constraint).
Which of the goals is assigned the highest priority?
A) goal 1
B) goal 2
C) goal 3
D) goals 2 and 3
E) All goals have the same priority.
Table 10-5
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
66) Table 10-5 represents a solution for
an integer programming problem. If this problem had been solved as a simple
linear programming problem, what would you expect the value of the objective
function to be?
A) less than 208
B) greater than 208
C) exactly 208
D) A or C
E) B or C
67) Table 10-5 represents a solution for
an integer programming problem. If one uses the optimal solution presented, how
much slack is there in the first equation?
A) 0 units
B) 5 units
C) 3 units
D) 2 units
E) None of the above
68) A model containing a linear objective
function and requiring that one or more of the decision variables take on an
integer value in the final solution is called
A) an integer programming problem.
B) a goal programming problem.
C) a nonlinear programming problem.
D) a multiple objective LP problem.
E) insufficient information.
Table 10-6
The profit function for a set of two
electronics products can be expressed by the following expression: X12 -2X1 -3X2 + 2X22 where X1 = the number of product 1 units produced and X2 = the number of product 2 units produced. At
least 10 units of X1 must be produced and at least
20 units of X2 must be produced. No more than 50 units total
can be produced.
69) What type of mathematical programming
model is required for the problem described in Table 10-6?
A) An integer programming model
B) A goal programming model
C) A nonlinear programming model
D) A zero-one integer programming model
E) A mixed-integer programming model
70) According to Table 10-6, how is the
constraint expressed that no more than 50 units can be produced?
A) X1 + X2 ? 50
B) X1 + X2 ? 50
C) X12 + X22? 50
D) X12 + X22? 50
E) X1 + X2 = 5051) A quadratic programming problem
involves which of the following conditions?A) squared terms in the objective function
and linear constraintsB) linear objective function and squared
terms in the constraintsC) squared terms in both the objective
function and constraintsD) a strictly goal programming problem
with squared terms in the objective functionE) None of the above52) Which of the following statements is false
concerning goal programming?A) The objective function is the main
difference between linear programming and goal programming.B) The objective in goal programming is to
minimize deviational variables.C) Deviational variables are zero if a
goal is completely obtained.D) It is not possible for two goals to
have equal priority.E) The priorities of each goal are
reflected in the objective function.53) Consider the following 0-1 integer
programming problem:.jpg”>If we wish to add the constraint that no
more than two of these variables must be positive, how would this be written?A) 2X + 2Y + 2Z ? 3B) X + Y + Z ? 2C) X ? 2, and Y ? 2, and Z ? 2D) X, Y, Z ? 2E) None of the above54) Consider the following 0 – 1 integer
programming problem:.jpg”>If we wish to add the constraint that X
must be positive, and that only Y or Z, but not both, can be positive, how
would the additional constraint(s) be written?A) X + Y + Z ? 3, Y + Z ? 1B) X ? 1, Y + Z = 1C) X ? 2, and Y ? 2, and Z ? 2D) X = 1, Y + Z ? 1E) None of the above55) 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. Which of the following must be
true for the optimal integer solution to this problem?A) X = 12 Y = 32B) X = 12 Y = 33C) X = 12D) Y = 32E) None of the above56) The overall best solution in a
nonlinear program is a A) global optimum.B) local optimum.C) binary optimum.D) nonlinear optimum.E) goal optimum.57) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a cost 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 cost of $2,400 and no idle
time. What was the value for the objective function for this goal programming
problem?A) 2300B) 100C) -100D) 0E) None of the above58) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a cost of
$3,600 and goal number 2 was to have no wasted material. The optimal solution
to this problem resulted in a cost of $3,900 and no wasted material. What was
the value for the objective function for this goal programming problem?A) 300B) -300C) 3300D) 0E) None of the aboveTable 10-3A 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 + 9000X3Subject
to: X1 + X2 + X3 ? 2 Constraint
1 -X1 + X2 ? 0 Constraint
2 25,000 X1 + 32,000 X2 + 29,000 X3 ? 62,000 (budget
limit) 16 X1 + 14 X2 + 19 X3 ? 36 (resource
limitation) all variables = 0
or 1where 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 otherwiseSolution x1 = 1, x2 = 0, x3 = 1, objective value = 14,000.59) Table 10-3 presents an integer
programming problem. What is the meaning of Constraint 1?A) If X1 is selected, X2 must also be selected.B) No more than two alternatives may be
selected.C) At least two alternatives must be
selected.D) If X2 is selected, X1 must also be selected.E) None of the above60) Table 10-3 presents an integer
programming problem. What is the meaning of Constraint 2?A) Both alternatives 1 and 2 must be
selected.B) If alternative 2 is selected,
alternative 1 must also be selected.C) Either alternative 1 or alternative 2
must be selected.D) No more than one alternative may be
selected.E) None of the above61) Table 10-3 presents an integer
programming problem. If the optimal solution is used, then only two of the
alternatives would be selected. How much slack would there be in the third
constraint?A) 1000B) 5000C) 3300D) 8000E) None of the above62) Table 10-3 presents an integer
programming problem. Suppose you wish to add a constraint that stipulates that
both alternative 2 and alternative 3 must be selected, or neither can be
selected. How would this constraint be written?A) X2 = X3B) X2 ? X3C) X2 ? X3D) X2 + X3 = 1E) None of the aboveTable 10-4.jpg”>63) Table 10-4 represents a solution to a
goal programming problem. There are three goals (each represented by a
constraint). Which goals are only partly achieved?A) number 1 onlyB) number 1 and number 2C) number 2 and number 3D) number 1 and number 3E) None of the above64) Table 10-4 represents a solution to a
goal programming problem. There are three goals (each represented by a
constraint). Goal number 3 represents a resource usage goal. How much of this
resource would be used by this solution?A) 50 unitsB) 70 unitsC) 2500 unitsD) 240 unitsE) None of the above65) Table 10-4 represents a solution to a
goal programming problem. There are three goals (each represented by a constraint).
Which of the goals is assigned the highest priority?A) goal 1B) goal 2C) goal 3D) goals 2 and 3E) All goals have the same priority.Table 10-5Maximize Z = 34 X1 + 43 X2 + 29 X3Subject 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-negativeFinal Integer
Solution: Z = 208 Decision Variable Solution X1 1 X2 0 X3 666) Table 10-5 represents a solution for
an integer programming problem. If this problem had been solved as a simple
linear programming problem, what would you expect the value of the objective
function to be?A) less than 208B) greater than 208C) exactly 208D) A or CE) B or C67) Table 10-5 represents a solution for
an integer programming problem. If one uses the optimal solution presented, how
much slack is there in the first equation?A) 0 unitsB) 5 unitsC) 3 unitsD) 2 unitsE) None of the above68) A model containing a linear objective
function and requiring that one or more of the decision variables take on an
integer value in the final solution is calledA) an integer programming problem.B) a goal programming problem.C) a nonlinear programming problem.D) a multiple objective LP problem.E) insufficient information.Table 10-6The profit function for a set of two
electronics products can be expressed by the following expression: X12 -2X1 -3X2 + 2X22 where X1 = the number of product 1 units produced and X2 = the number of product 2 units produced. At
least 10 units of X1 must be produced and at least
20 units of X2 must be produced. No more than 50 units total
can be produced. 69) What type of mathematical programming
model is required for the problem described in Table 10-6?A) An integer programming modelB) A goal programming modelC) A nonlinear programming modelD) A zero-one integer programming modelE) A mixed-integer programming model 70) According to Table 10-6, how is the
constraint expressed that no more than 50 units can be produced?A) X1 + X2 ? 50B) X1 + X2 ? 50C) X12 + X22? 50D) X12 + X22? 50E) X1 + X2 = 50
