MAT 540 Quiz 5. 20/20. Get an A++. - 63161

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Question 1

 

In a mixed integer model, some solution values for decision variables are integer and others are

only 0 or 1.

 

Question 2

 

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.

 

Question 3

 

Rounding non]integer solution values up to the nearest integer value will result in an infeasible

solution to an integer linear programming problem.

 

Question 4

 

The solution to the LP relaxation of a maximization integer linear program provides an upper

bound for the value of the objective function.

 

Question 5

 

A conditional constraint specifies the conditions under which variables are integers or real

variables.

 

Question 6

 

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.

 

Question 7

 

Max Z = 5x1 + 6x2

Subject to: 17x1 + 8x2 . 136

3x1 + 4x2 . 36

x1, x2 . 0 and integer

What is the optimal solution?

 

Question 8

 

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.

 

Question 9

 

If we are solving a 0]1 integer programming problem, the constraint x1 + x2 . 1 is a __________

constraint.

 

Question 10

 

In a __________ integer model, some solution values for decision variables are integers and

others can be non]integer.

 

Question 11

 

If we are solving a 0]1 integer programming problem, the constraint x1 . x2 is a

__________ constraint.

 

Question 12

 

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?

 

Question 13

 

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

 

Question 14

 

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

 

Question 15

 

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.

 

Question 16

 

In a 0]1 integer programming model, if the constraint x1]x2 = 0, it means when project 1 is

selected, project 2 __________ be selected.

 

Question 17

 

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

solution is

 

Question 18

 

If we are solving a 0]1 integer programming problem, the constraint x1 + x2 = 1 is a __________

constraint.

 

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

 

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

Solution Description

Question 1

 

In a mixed integer model, some solution values for decision variables are integer and others are

only 0 or 1.

 

Question 2

 

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.

 

Question 3

 

Rounding non]integer solution values up to the nearest integer value will result in an infeasible

solution to an integer linear programming problem.

 

Question 4

 

The solution to the LP relaxation of a maximization integer linear program provides an upper

bound for the value of the objective function.

 

Question 5

 

A conditional constraint specifies the conditions under which variables are integers or real

variables.

 

Question 6

 

If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3

separate constraint

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