Strayer MAT540 week 10 quiz 5

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, x2 + x5
? 1

x1 – x5 ? 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
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