Question 1

Which of the following is true about generating alternatives in binary optimization?

Accepted Answer

A)  If the second-best solution is very close to optimal, it is always preferred over the true optimal solution because of factors outside the model. 
B)  If alternative solutions exist, it would not help management because some factors that make one alternative are not preferred over the factors that make another alternative. 
C)  If the solution is a unique optimal solution, it would be good for management to know how much worse the second-best solution is than the unique optimal solution. 
D)  If any alternative solution exists, it would only be a second-best next to the optimal solution because there is no third-best or an alternative second-best solution to any binary integer programming problem. 
A)  If the second-best solution is very close to optimal, it is always preferred over the true optimal solution because of factors outside the model. 
B)  If alternative solutions exist, it would not help management because some factors that make one alternative are not preferred over the factors that make another alternative. 
C)  If the solution is a unique optimal solution, it would be good for management to know how much worse the second-best solution is than the unique optimal solution. 
D)  If any alternative solution exists, it would only be a second-best next to the optimal solution because there is no third-best or an alternative second-best solution to any binary integer programming problem.

Question 2

A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant has two machines, Machine-1 and Machine-2, and both of them are used to make the rubber strips. Machine-1 is available 180 hours per month and Machine-2 is available 200 hours per month. Manufacturing one strip of Butadiene requires 2.75 hours on Machine-1 and 3 hours on Machine-2. For processing one strip of Polyisoprene, it takes 3.5 hours on Machine-1 and 4 hours on Machine-2. Formulate an all-integer model that will determine how many units of each type of the rubber should be used to maximize the manufacturer's contribution to profit if he gets a profit of $20 on Butadiene and $26 on Polyisoprene?

Accepted Answer

Let B = Number of units of But

Question 3

A coffee manufacturing company has two different plants that roast imported coffee beans. After roasting, the plants produce three types of coffee beans, A, B, and C. The company has contracted with a chain of cafes to provide per week, 20 tons of coffee bean A, 11 tons of coffee bean B, and 18 tons of coffee bean C. The two plants have the same capacity, but diverse operational features as below:
   
Formulate and solve all-integer model that will determine how many tons of each type of coffee beans are produced in each plant by minimizing the total cost.

Accepted Answer

Let Xᵢⱼ = number of tons of coffee beans

Question 4

The sum of two or more binary variables must be less than or equal to one in _____ constraint.

Accepted Answer

A)  corequisite 
B)  conditional 
C)  multiple-choice 
D)  mutually exclusive 
A)  corequisite 
B)  conditional 
C)  multiple-choice 
D)  mutually exclusive

Question 5

Binary variables are identified with the _____designation in the Solver Parameters dialog box.

Accepted Answer

A)  bin 
B)  0 and 1 
C)  int 
D)  dif 
A)  bin 
B)  0 and 1 
C)  int 
D)  dif

Question 6

Four shipping containers can altogether take a maximum of 20 tons for one shipment order. The following table provides details on the weight (in tons) and value of each container:
   
Develop a binary integer model that will determine the two containers and the quantity that should be considered for shipment using these two containers to maximize the value of the shipment.

Accepted Answer

Let C₁ = if Container 1 is considered fo

Question 7

The objective function for a linear optimization problem is: Max 3x + 5y, with one of the constraints being x, y ≥ 0 and integer. x and y are the only decisions variables. This is an example of a(n) _____.

Accepted Answer

A)  all-integer linear program 
B)  mixed-integer linear program 
C)  nonlinear program 
D)  binary integer linear program 
A)  all-integer linear program 
B)  mixed-integer linear program 
C)  nonlinear program 
D)  binary integer linear program

Question 8

The optimal solution to the integer program will be an extreme point of the _____.

Accepted Answer

A)  convex hull 
B)  objective contour 
C)  cutting plane 
D)  slope 
A)  convex hull 
B)  objective contour 
C)  cutting plane 
D)  slope

Question 9

The following questions refer to an advertisement budgeting problem involving printing of five magazines represented by binary variables M1, M2, M3, M4, and M5.a. Write a constraint modeling a situation in which two of the magazines M1, M4, and M5 must be printed.
b. Write a constraint modeling a situation in which, if M2 or M3 is printed, they must both be printed.
c. Write a constraint modeling a situation in which magazine M1 or M3 must be printed, but not both.
d. Write constraints modeling a situation where M2 cannot be printed unless magazine M3 and M5 also are printed.
e. Write a constraint in which not more than 4 of all the five magazines have to be printed.
f. Write a constraint in which exactly five of the magazines are printed.

Accepted Answer

a. M1 + M4 + M5 = 2
b. M2 - M3

Question 10

The part-worth for each of the attribute levels in a conjoint analysis is determined by _____.

Accepted Answer

A)  regression analysis 
B)  sensitivity analysis 
C)  online surveys 
D)  word-of-mouth 
A)  regression analysis 
B)  sensitivity analysis 
C)  online surveys 
D)  word-of-mouth

Question 11

A binary mixed-integer programming problem in which the binary variables represent whether an activity, such as a production run, is undertaken or not is known as the _____.

Accepted Answer

A)  capital budgeting problem 
B)  share of choice problem 
C)  fixed-cost problem 
D)  covering problem 
A)  capital budgeting problem 
B)  share of choice problem 
C)  fixed-cost problem 
D)  covering problem

Question 12

A coffee maker vendor has set up two coffee machines, Machine 1 and Machine 2, inside an organization. The service cost incurred on Machine 1 and Machine 2 is $100 and $80, respectively. The production cost of coffee is $2 per mug for Machine 1 and $3 per mug for Machine 2. There is no service provided by the vendor on Sundays. The weekly production capacity is 1000 mugs for Machine 1 and 1200 mugs for Machine 2, and thereafter the machine needs to be serviced before any extra mug of coffee is to be served. Due to Christmas, the employee attendance at the organization is going to be low and only one machine has to be used to serve at least 800 mugs of coffee in that week in order to minimize the total cost.
Formulate and solve the integer programming model that could be used to determine the coffee machine which minimizes the cost.

Accepted Answer

A = 1 if Machine 1 is used to serve coff

Question 13

The objective function for an optimization problem is: Min 3x - 2y, with one of the constraints being x, y ≥ 0 and integer. If the integer restriction on the variables is removed, this would be a familiar two-variable linear program; however, it would be an example of _____.

Accepted Answer

A)  convex hull of the linear program 
B)  a mixed-integer linear program 
C)  LP relaxation of the integer linear program 
D)  a binary integer linear program 
A)  convex hull of the linear program 
B)  a mixed-integer linear program 
C)  LP relaxation of the integer linear program 
D)  a binary integer linear program

Question 14

The _____ is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model.

Accepted Answer

A)  weightage 
B)  share of choice 
C)  part-worth 
D)  share of market 
A)  weightage 
B)  share of choice 
C)  part-worth 
D)  share of market

Question 15

In cases where Excel Solver experiences excessive run times when solving integer linear problems, the Integer Optimality is set to _____.

Accepted Answer

A)  5% 
B)  0% 
C)  infinity 
D)  a value equal to the number of integer constraints 
A)  5% 
B)  0% 
C)  infinity 
D)  a value equal to the number of integer constraints

Question 16

Which of the following approaches to solving integer linear optimization problems tries to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points?

Accepted Answer

A)  Branch-and bound approach 
B)  Cutting plane approach 
C)  Trial-and-error approach 
D)  Convex hull approach 
A)  Branch-and bound approach 
B)  Cutting plane approach 
C)  Trial-and-error approach 
D)  Convex hull approach

Question 17

In order to choose the best solution for implementation, practitioners usually recommend re-solving the integer linear program several times with variations in the_____.

Accepted Answer

A)  objective function 
B)  decision variables 
C)  constraint coefficients 
D)  integer constraints 
A)  objective function 
B)  decision variables 
C)  constraint coefficients 
D)  integer constraints

Question 18

Which of the following is a likely constraint on the production quantity x associated with a maximum value and a setup variable y in a fixed-cost problem?

Accepted Answer

A)  x ≥ My 
B)  x ≤ My 
C)  Mx ≤ y 
D)  xy ≥ M 
A)  x ≥ My 
B)  x ≤ My 
C)  Mx ≤ y 
D)  xy ≥ M

Question 19

A chocolate making company largely produces one particular type of crunchy chocolate bar. There are two machines in the plant that produces this chocolate bar. The maintenance costs per day incurred on these two machines are $100 and $120, respectively. The manufacturing cost per chocolate bar is $2.5 for Machine-1 and $2 for Machine-2. The maximum daily production capacity for Machine-1 and Machine-2 are 1100 and 1250, respectively, and the company must produce at least 1000 chocolate bars per day. Develop and solve an integer programming model for minimizing the total cost.

Accepted Answer

Let C₁ = the number of chocolate bars pr

Question 20

Andrew is ready to invest $200,000 in stocks and he has been provided nine different alternatives by his financial consultant. The following stocks belong to three different industrial sectors and each sector has three varieties of stocks each with different expected rate of return. The average rate of return taken for the past ten years is provided with each of the nine stocks.
   
The decision will be based on the constraints provided below:
-Exactly 5 alternatives should be chosen.
-Any stock chosen can have a maximum investment of $55,000.
-Any stock chosen must have a minimum investment of at least $25,000.
-For the Airlines sector, the maximum number of stocks that can be chosen is two.
-The total amount invested in Banking must be at least as much as the amount invested in Agriculture.
Formulate and solve a model that will decide Andrew's investment strategy to maximize his expected annual return.

Accepted Answer

Let X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, and

Which of the following is true about generating alternatives in binary optimization?

The sum of two or more binary variables must be less than or equal to one in _____ constraint.

Binary variables are identified with the _____designation in the Solver Parameters dialog box.

The objective function for a linear optimization problem is: Max 3x + 5y, with one of the constraints being x, y ≥ 0 and integer. x and y are the only decisions variables. This is an example of a(n) _____.

The optimal solution to the integer program will be an extreme point of the _____.

The part-worth for each of the attribute levels in a conjoint analysis is determined by _____.

A binary mixed-integer programming problem in which the binary variables represent whether an activity, such as a production run, is undertaken or not is known as the _____.

The objective function for an optimization problem is: Min 3x - 2y, with one of the constraints being x, y ≥ 0 and integer. If the integer restriction on the variables is removed, this would be a familiar two-variable linear program; however, it would be an example of _____.

The _____ is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model.

In cases where Excel Solver experiences excessive run times when solving integer linear problems, the Integer Optimality is set to _____.

Which of the following approaches to solving integer linear optimization problems tries to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points?

In order to choose the best solution for implementation, practitioners usually recommend re-solving the integer linear program several times with variations in the_____.

Which of the following is a likely constraint on the production quantity x associated with a maximum value and a setup variable y in a fixed-cost problem?

Introduction

Descriptive Statistics

Data Visualization

Linear Regression

Time Series Analysis and Forecasting

Data Mining

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Linear Optimization Models

Nonlinear Optimization Models

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Exam 9: Integer Linear Optimization Models

Which of the following is true about generating alternatives in binary optimization?

The sum of two or more binary variables must be less than or equal to one in _____ constraint.

Binary variables are identified with the _____designation in the Solver Parameters dialog box.

The objective function for a linear optimization problem is: Max 3x + 5y, with one of the constraints being x, y ≥ 0 and integer. x and y are the only decisions variables. This is an example of a(n) _____.

The optimal solution to the integer program will be an extreme point of the _____.

The part-worth for each of the attribute levels in a conjoint analysis is determined by _____.

A binary mixed-integer programming problem in which the binary variables represent whether an activity, such as a production run, is undertaken or not is known as the _____.

The objective function for an optimization problem is: Min 3x - 2y, with one of the constraints being x, y ≥ 0 and integer. If the integer restriction on the variables is removed, this would be a familiar two-variable linear program; however, it would be an example of _____.

The _____ is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model.

In cases where Excel Solver experiences excessive run times when solving integer linear problems, the Integer Optimality is set to _____.

Which of the following approaches to solving integer linear optimization problems tries to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points?

In order to choose the best solution for implementation, practitioners usually recommend re-solving the integer linear program several times with variations in the_____.

Which of the following is a likely constraint on the production quantity x associated with a maximum value and a setup variable y in a fixed-cost problem?

Introduction

Descriptive Statistics

Data Visualization

Linear Regression

Time Series Analysis and Forecasting

Data Mining

Spreadsheet Models

Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters