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1. The solution to the LP relaxation of a maximization integer linear program provides anupper bound for the value of the objective function.

Answer 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.

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

constraintx1 +x2 1 is a mutually exclusive constraint.

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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.If we are solving a 0-1 integer programming problem, the constraintx1 x2 is a

conditional constraint.

Answer True

False

2 points

Question 7

1.If we are solving a 0-1 integer programming problem, the constraintx1 +x2 1 is a__________ constraint.

Answer

multiple choice

mutually exclusive

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conditional

corequisite

2 points

Question 8

1.If the solution values of a linear program are rounded in order to obtain an integersolution, 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 9

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 10

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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 andS3 will prevent you from exploring site S7.

Restriction 2. Evaluating sites S2or

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 11

1.In a __________ integer model, some solution values for decision variables are integersand others can be non-integer.

Answer

total

0 - 1

mixed

all of the above

2 points

Question 12

1.Max Z = 5x1 + 6x2

Subject to: 17x1 + 8x2 1363x1 + 4x2 36

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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 13

1.In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5cannot 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 14

1.If we are solving a 0-1 integer programming problem, the constraintx1 +x2 = 1 is a

__________ constraint.

Answer

multiple choice

mutually exclusive

conditional

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corequisite

2 points

Question 15

1.Binary variables are

Answer

0 or 1 only

any integer value

any continuous valueany negative integer value

2 points

Question 16

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 andS3 will prevent you from exploring site S7.

Restriction 2. Evaluating sites S2 orS4 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 17

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1.If we are solving a 0-1 integer programming problem, the constraintx1 =x2 is a__________ constraint.

Answer

multiple choice

mutually exclusive

conditional

corequisite

2 points

Question 18

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 thesemachines 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 19

1.

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Consider the following integer linear programming problem

Max Z = 3x1 + 2x2Subject to: 3x1 + 5x2 30

4x1 + 2x2 28

x1 8x1 , x2 0 and integerWhat is the optimal solution? Write your answer in the form : ( x1, x2, z). (For example,

the expression (10, 20, 50) means that x1 = 10, x2 = 20, and z = 50).

Answer

2 points

Question 20

1.Consider the following integer linear programming problem

Max Z = 3x1 + 2x2

Subject to: 3x1 + 5x2 305x1 + 2x2 28

x1 8

x1 ,x2 0 and integer

What is the optimal solution? Write your answer in the form : ( x1, x2, z)