MAT540 - Week 9 - Quiz 5 - A+ Solution - 41123

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Question 1

 

1.

 

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

AnswerTrue

False

 

Question 2

 

1.

 

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 can not be selected.

AnswerTrue

False

 

Question 3

 

1.

 

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

AnswerTrue

False

 

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.

AnswerTrue

False

 

Question 5

 

1.

 

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

AnswerTrue

False

 

Question 6

 

1.

 

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

AnswerTrue

False

 

Question 7

 

1.

 

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

 

Question 8

 

1.

 

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

Answer

 

multiple choice

 

mutually exclusive

 

conditional

 

corequisite

 

Question 9

 

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, 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

 

Question 10

 

1.

 

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

 

Question 11

 

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 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

 

Question 12

 

1.

 

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

 

Question 13

 

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 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.

Answer

 

Y1 + Y4 ? 0

 

Y1 + Y4 = 0

 

Y1 + Y4 ? 1

 

Y1 + Y4 ? 0

 

Question 14

 

1.

 

Max Z = 5x1 + 6x2

Subject to: 17x1 + 8x2 ? 136

3x1 + 4x2 ? 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

 

Question 15

 

1.

 

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

 

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