Question details

Mat 540 Week 9 Quiz 5
$ 15.00

 

Question 1 

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

Answer

True

false
 2 points  

Question 2 

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

True

False

Question 3

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

True

False

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

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

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.
Answer

True

False

2 points  

Question 7

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 8

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.
 
https://blackboard.strayer.edu/courses/1/MAT540049VA016-1136-001/ppg/respondus/exam_Quiz_5/image0024ecbcc96.jpg
 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 9  

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 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.
 
https://blackboard.strayer.edu/courses/1/MAT540049VA016-1136-001/ppg/respondus/exam_Quiz_5/image0014ecbcc96.jpg
 
 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 11

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

Answer

total

0 – 1

Mixed

all of the above

2 points  

Question 12 

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

Answer

S2 +S5 ≤ 1

S4 +S5 ≤ 1

S2 +S5 + S4 +S5 ≤ 2

S2 +S5 ≤ 1,  S4 +S5 ≤ 1

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.

Answer

exactly 2

at least 2

at most 2

none of the above

2 points  

Question 14

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 15

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 16

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 17

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

2 points  

Question 18  

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 19

Max Z =   3x1 + 5x2
Subject to:      7x1 + 12x2 ≤ 136
                       3x1 + 5x2 ≤ 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 =      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
Answer

 

 

 

Available solutions
  • Mat 540 Week 9 Quiz 5
    $15.00

    Question 1 The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. Answer True false 2 points Question 2 A conditional constraint specifies the conditions under which variables are integers or real

    Submitted on: 11 Mar, 2016 01:39:40 This tutorial has not been purchased yet .