MAT540/MAT 540 QUIZ 5 WEEK 9

Question 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 2
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 3
If we are solving a 0-1 integer programming problem, the
constraint x1 ? x2 is a conditional constraint.
Answer
True
False
2 points
Question 4
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
If we are solving a 0-1 integer programming problem with
three decision variables, the constraint x1 + x2 + x3 ? 3
is a mutually exclusive constraint.
Answer
True
False
2 points
Question 6
A conditional constraint specifies the conditions under
which variables are integers or real variables.
Answer
True
False
2 points
Question 7
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 1, x2 + x5 ? 1
x1 – x5 ? 1 1, x2 – x5 ? 1
2 points
Question 8
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 9
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
Answer
S1 + S3 + S7 ? 1
S1 + S3 + S7?1
S1 + S3 + S7 = 2
S1 + S3 + S7? 2
2 points
Question 10
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 11
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 12
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 13
In a 0-1 integer programming model, if the constraint
x1-x2 = 0, it means when project 1 is selected, project 2 __________ be
selected.
Answer
can also
can sometimes
can never
must also
2 points
Question 14
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 15
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?
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 16
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 17
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 18
Binary variables are
Answer
0 or 1 only
any integer value
any continuous value
any negative integer value
2 points
Question 19
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
Answer
36
2 points
Question 20
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
22