Question 1

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.

True

False

2 points

Question 2

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 3

In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.

True

False

2 points

Question 4

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 5

In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1.

True

False

2 points

Question 6

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 cannot be selected.

True

False

2 points

Question 7

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 8

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 9

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 10

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 11

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

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is

always optimal and feasible

sometimes optimal and feasible

always optimal but not necessarily feasible

never optimal and feasible

2 points

Question 13

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 14

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 15

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?

x1 + x2 + x5 ≤ 1

x1 + x2 + x5 ≥1

x1 + x5 ≤ 1,  x2 + x5 ≤ 1

x1 - x5 ≤ 1,  x2 - x5 ≤ 1

2 points

Question 16

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 17

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 18

Binary variables are

0 or 1 only

any integer value

any continuous value

any negative integer value

2 points

Question 19

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

2 points

Question 20

Consider the following integer linear programming problem

Max Z =      3x1 + 2x2
Subject to:   3x1 + 5x2 ≤ 30
4x1 + 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

2 points

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MAT 540/MAT540 WEEK 10 QUIZ QUANTITATIVE METHODS (100% ANSWER)
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