QUESTION 1
1. The
solution to the LP relaxation of a maximization integer linear program provides
an upper bound for the value of the objective function.
True
False
2 points
QUESTION 2
1. If
exactly 3 projects are to be selected from a set of 5 projects, this would be
written as 3 separate constraints in an integer program.
True
False
2 points
QUESTION 3
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.
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.
True
False
2 points
QUESTION 5
1. A
conditional constraint specifies the conditions under which variables are
integers or real variables.
True
False
2 points
QUESTION 6
1. Rounding
non-integer solution values up to the nearest integer value will result in an
infeasible solution to an integer linear programming problem.
True
False
2 points
QUESTION 7
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.
exactly
2
at
least 2
at most
2
none of
the above
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 a constraint to ensure that if machine 4 is used,
machine 1 will not be used.
Y1 + Y4
? 0
Y1 + Y4
= 0
Y1 + Y4
? 1
Y1 + Y4
? 0
2 points
QUESTION 9
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
S2 +S5
? 1
S4 +S5
? 1
S2 +S5
+ S4 +S5 ? 2
S2 +S5
? 1, S4 +S5 ? 1
2 points
QUESTION 10
1. Binary
variables are
0 or 1
only
any
integer value
any
continuous value
any
negative integer value
2 points
QUESTION 11
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, the constraint for
the first restriction is
S1 + S3
+ S7 ? 1
S1 + S3
+ S7 ?1
S1 + S3
+ S7 = 2
S1 + S3
+ S7 ? 2
2 points
QUESTION 12
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.
Y1 + Y2
+ Y3+ Y4 ? 3
Y1 + Y2
+ Y3+ Y4 = 3
Y1 + Y2
+ Y3+ Y4 ?3
none of
the above
2 points
QUESTION 13
1. In a 0-1
integer programming model, if the constraint x1-x2 = 0, it means when project 1
is selected, project 2 __________ be selected.
can
also
can
sometimes
can
never
must
also
2 points
QUESTION 14
1. In a 0-1
integer programming model, if the constraint x1-x2 ? 0, it means when project 2
is selected, project 1 __________ be selected.
must
always
can
sometimes
can
never
A and B
2 points
QUESTION 15
1. Max Z =
5×1 + 6×2
Subject to: 17×1 + 8×2 ? 136
3×1
+ 4×2 ? 36
x1,
x2 ? 0 and integer
What is the optimal solution?
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 16
1. If we are
solving a 0-1 integer programming problem, the constraint x1 = x2 is a
__________ constraint.
multiple
choice
mutually
exclusive
conditional
corequisite
2 points
QUESTION 17
1. In a
__________ integer model, some solution values for decision variables are
integers and others can be non-integer.
total
0 – 1
mixed
all of
the above
2 points
QUESTION 18
1. If we are
solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a
__________ constraint.
multiple
choice
mutually
exclusive
conditional
corequisite
2 points
QUESTION 19
1. Max Z
= 3×1 + 5×2
Subject to: 7×1 +
12×2 ? 136
3×1 + 5×2 ? 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
2 points
QUESTION 20
1. Consider
the following integer linear programming problem
Max Z = 3×1 + 2×2
Subject to: 3×1 +
5×2 ? 30
5×1 + 2×2 ? 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
