1. The solution to the LP relaxation of a maximization integer
linear program provides an upper bound for the value of the
objective function.
Answer
True
False
2 points
Question 2
1.
A conditional constraint specifies the conditions under
which variables are integers or real variables.
Answer
True
False
2 points
Question 3
1.
In a mixed integer model, some solution values for decision
variables are integer and others are only 0 or 1.
Answer
True
False
2 points
Question 4
1.
If we are solving a 0-1 integer programming problem with
three decision variables, the constraint x1 + x2 ≤ 1 is a
mutually exclusive constraint.
Answer
True
False
2 points
Question 5
1.
Rounding non-integer solution values up to the nearest
integer value will result in an infeasible solution to an
integer linear programming problem.
Answer
True
False
2 points
Question 6
1.
In a 0-1 integer programming problem involving a capital
budgeting application (where xj = 1, if project j is selected,
xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if
project 2 is selected, project 1 can not be selected.
Answer
True
False
2 points
Question 7
1.
If we are solving a 0-1 integer programming problem, the
constraint x1 ≤ x2 is a __________ constraint.
Answer
multiple choice
mutually exclusive
conditional
corequisite
2 points
Question 8
1.
The Wiethoff Company has a contract to produce 10000
garden hoses for a customer. Wiethoff has 4 different
machines that can produce this kind of hose. Because these
machines are from different manufacturers and use
differing technologies, their specifications are not the same.
Write the constraint that indicates they can purchase no
more than 3 machines.
Answer
Y1 + Y2 + Y3+ Y4 ≤ 3
Y1 + Y2 + Y3+ Y4 = 3
Y1 + Y2 + Y3+ Y4 ≥3
none of the above
2 points
Question 9
1.
If we are solving a 0-1 integer programming problem, the
constraint x1 = x2 is a __________ constraint.
Answer
multiple choice
mutually exclusive
conditional
corequisite
2 points
Question 10
1.
The Wiethoff Company has a contract to produce 10000
garden hoses for a customer. Wiethoff has 4 different
machines that can produce this kind of hose. Because these
machines are from different manufacturers and use
differing technologies, their specifications are not the same.
Write a constraint to ensure that if machine 4 is used,
machine 1 will not be used.
Answer
Y1 + Y4 ≤ 0
Y1 + Y4 = 0
Y1 + Y4 ≤ 1
Y1 + Y4 ≥ 0
2 points
Question 11
1.
In a __________ integer model, some solution values for
decision variables are integers and others can be noninteger.
Answer
total
0-1
mixed
all of the above
2 points
Question 12
1.
You have been asked to select at least 3 out of 7 possible
sites for oil exploration. Designate each site as S1, S2, S3,
S4, S5, S6, and S7. The restrictions are:
Restriction 1. Evaluating sites S1 and S3 will prevent
you from exploring site S7.
Restriction 2. Evaluating sites S2 or
S4 will prevent you from assessing site S5.
Restriction 3. Of all the sites, at least 3 should be
assessed.
Assuming that Si is a binary variable, write the
constraint(s) for the second restriction
Answer
S2 +S5 ≤ 1
S4 +S5 ≤ 1
S2 +S5 + S4 +S5 ≤ 2
S2 +S5 ≤ 1, S4 +S5 ≤ 1
2 points
Question 13
1.
Assume that we are using 0-1 integer programming model
to solve a capital budgeting problem and xj = 1 if project j
is selected and xj = 0, otherwise.
The constraint (x1 + x2 + x3 + x4 ≤ 2) means that
__________ out of the 4 projects must be selected.
Answer
exactly 2
at least 2
at most 2
none of the above
2 points
Question 14
1.
The solution to the linear programming relaxation of a
minimization problem will always be __________ the
value of the integer programming minimization problem.
Answer
greater than or equal to
less than or equal to
equal to
different than
2 points
Question 15
1.
If the solution values of a linear program are rounded in
order to obtain an integer solution, the solution is
Answer
always optimal and feasible
sometimes optimal and feasible
always optimal but not necessarily feasible
never optimal and feasible
2 points
Question 16
1.
If we are solving a 0-1 integer programming problem, the
constraint x1 + x2 ≤ 1 is a __________ constraint.
Answer
multiple choice
mutually exclusive
conditional
corequisite
2 points
Question 17
1.
Max Z = 5x1 + 6x2
Subject to: 17x1 + 8x2 ≤ 136
3x1 + 4x2 ≤ 36
x1, x2 ≥ 0 and integer
What is the optimal solution?
Answer
x1 = 6, x2 = 4, Z = 54
x1 = 3, x2 = 6, Z = 51
x1 = 2, x2 = 6, Z = 46
x1 = 4, x2 = 6, Z = 56
2 points
Question 18
1.
In a capital budgeting problem, if either project 1 or project
2 is selected, then project 5 cannot be selected. Which of
the alternatives listed below correctly models this situation?
Answer
x1 + x2 + x5 ≤ 1
x1 + x2 + x5 ≥1
x1 + x5 ≤ 1, x2 + x5 ≤ 1
x1 - x5 ≤ 1, x2 - x5 ≤ 1
2 points
Question 19
1.
Max Z = 3x1 + 5x2
Subject to:
7x1 + 12x2 ≤ 136
3x1 + 5x2 ≤ 36
x1, x2 ≥ 0 and integer
Find the optimal solution. What is the value of the
objective function at the optimal solution. Note: The
answer will be an integer. Please give your answer as
an integer without any decimal point. For example,
25.0 (twenty-five) would be written 25
Answer
2 points
Question 20
1.
Consider the following integer linear programming
problem
Max Z = 3x1 + 2x2
Subject to: 3x1 + 5x2 ≤ 30
5x1 + 2x2 ≤ 28
x1 ≤ 8
x1 ,x2 ≥ 0 and integer
Find the optimal solution. What is the value of the
objective function at the optimal solution. Note: The
answer will be an integer. Please give your answer as
an integer without any decimal point. For example,
25.0 (twenty-five) would be written 25
Answer