Question 1

A shipping freighter has space for two more shipping containers, but the combined weight cannot go over 20 tons. Four shipping containers are being considered. The following table provides details on the weight (in tons) and value of the contents of each container. $$\begin{array} { l l l l l } 
\text { Container } & 1 & 2 & 3 & 4 \
\hline \text { Weight of container (tons) } & 5 & 6 & 9 & 7 \
\hline \text { Value/Container } & \$ 6000 & \$ 5500 & \$ 7500 & \$ 6000
\end{array}$$ ​
Develop a binary integer model that will determine the two containers that will maximize the value of the shipment.

Accepted Answer

Let C₁ = if Container 1 is considered for shipment; 0 otherwise C₂ = if Container 2 is considered for shipment; 0 otherwise C₃ = if Container 3 is considered for shipment; 0 otherwise C₄ = if Container 4 is considered for shipment; 0 otherwise Max 6000C₁ + 5500C₂ + 7500C₃ + 6000C₄ s.t. 5C₁ + 6C₂ + 9C₃ + 7C₄ £ 20 C₁ + C₂ + C₃ + C₄ = 2 C_i = 0, 1 (for i = 1, 2, 3, 4)

Question 2

For a location problem, if the variables are defined as xi = 1 if an outlet store is established in region i and 0 otherwise, the objective function is best defined by __________ for i = 1, 2, …, n number of outlet stores included in the problem.

Accepted Answer

A)  Min(Sxi) 
B)  Max(Sxi) 
C)  Min(pxi) 
D)  Max(pxi)  A

Question 3

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. What category does the above objective fall under?

Accepted Answer

A)  Capital budgeting problem
B)  Covering problem
C)  Fixed-cost problem
D)  Product design and market share optimization problem D

Question 4

The importance of _________ for integer linear programming problems is often intensified by the fact that a small change in one of the coefficients in the constraints can cause a relatively large change in the value of the optimal solution.

Accepted Answer

A)  objective function
B)  decision variables
C)  sensitivity analysis
D)  optimization analysis

Question 5

Greenbell Software Inc. conducted a study on its smartphone products in the market to determine which phone has the best features in terms of three prominent attributes: operating system of the phone (A or B), RAM (512MB or 1GB), and the rear camera specifications (3MP, 5MP, or 7MP). A sample of eight customers participated in the study and provided the following part-worths for each of the above attributes.
​ $$\begin{array} { | c | c c | c c | c c c | } 
&{ \text { Operating System } } &&  { \text { RAM } } &&&  { \text { Camera } } \
\hline \text { Consumer } & \text { A } & \text { B } & 512 \mathrm { MB } & 1 \mathrm {~GB} & 3 \mathrm { MP } & 5 \mathrm { MP } & 7 \mathrm { MP } \
\hline 1 & 25 & 29 & 20 & 45 & 18 & 18 & 15 \
2 & 35 & 32 & 30 & 35 & 27 & 19 & 13 \
3 & 45 & 35 & 30 & 30 & 15 & 25 & 30 \
4 & 55 & 65 & 25 & 45 & 25 & 20 & 35 \
5 & 40 & 40 & 35 & 40 & 20 & 25 & 30 \
6 & 30 & 47 & 40 & 35 & 15 & 20 & 15 \
7 & 35 & 45 & 30 & 30 & 20 & 20 & 20 \
8 & 25 & 25 & 25 & 30 & 25 & 30 & 30 \
\hline
\end{array}$$ Suppose the overall utility (sum of part-worths) of the current favorite Greenbell smartphone is 100 for each consumer. What new product design will maximize the share of choice for the eight consumers in the sample?

Accepted Answer

The answer of Greenbell Software Inc. conducted a study on...

Question 6

A constraint involving binary variables that does not allow certain variables to equal one unless certain other variables are equal to one is known as a

Accepted Answer

A)  conditional constraint.
B)  corequisite constraint.
C)  k out of n alternatives constraint.
D)  mutually exclusive constraint.

Question 7

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. In an integer programming model for this problem, the available sizes of the trousers will be represented as

Accepted Answer

A)  binary variables
B)  constraints
C)  attributes
D)  regression constants

Question 8

Which of the following is true about the sensitivity analysis for integer optimization problems?

Accepted Answer

A)  Sensitivity reports are readily available for integer optimization problems similar to the linear programming problems.
B)  Because of the discrete nature of the integer optimization, Excel Solver takes much more time to calculate objective function coefficient ranges, shadow prices, and right-hand-side ranges.
C)  The sensitivity analysis is not important for integer problems.
D)  To determine the sensitivity of the solution to changes in model inputs for integer optimization problems, the data must be changed and the problem must be re-solved.

Question 9

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. $$\begin{array} { l c c } 
\text { Stock } & \text { Industry } & \text { Annual Return } \
\hline 1 & \text { Airlines } & 18.24 \% \
2 & \text { Airlines } & 28.75 \% \
3 & \text { Arrlines } & 11.08 \% \
4 & \text { Banking } & 20.12 \% \
5 & \text { Banking } & 14.00 \% \
6 & \text { Banking } & 26.17 \% \
7 & \text { Agriculture } & 23.67 \% \
8 & \text { Agriculture } & 18.25 \% \
9 & \text { Agriculture } & 16.50 \%
\end{array}$$ ​
The decision will be based on the constraints provided below:
o Exactly 5 alternatives should be chosen.
o One stock can have a maximum invest of $55,000.
o Any stock chosen must have a minimum investment of at least $25,000.
o For the Airlines sector, the maximum number of stocks chosen should be two.
o The total amount invested in Banking must be at least as much as the amount invested in Agriculture.
​
Formulate a model that will decide Andrew's investment strategy to maximize his expected annual return.

Accepted Answer

The answer of Andrew is ready to invest $200,000 in...

Question 10

Greenbell Software Inc. conducted a study on its smartphone products in the market to determine which phone has the best features in terms of three prominent attributes: operating system of the phone (A or B), RAM (512MB or 1GB), and the rear camera specifications (3MP, 5MP, or 7MP). A sample of eight customers participated in the study and provided the following part-worths for each of the above attributes.
​ $$\begin{array} { | c | c c | c c | c c c | } 
&{ \text { Operating System } } &&  { \text { RAM } } &&&  { \text { Camera } } \
\hline \text { Consumer } & \text { A } & \text { B } & 512 \mathrm { MB } & 1 \mathrm {~GB} & 3 \mathrm { MP } & 5 \mathrm { MP } & 7 \mathrm { MP } \
\hline 1 & 25 & 29 & 20 & 45 & 18 & 18 & 15 \
2 & 35 & 32 & 30 & 35 & 27 & 19 & 13 \
3 & 45 & 35 & 30 & 30 & 15 & 25 & 30 \
4 & 55 & 65 & 25 & 45 & 25 & 20 & 35 \
5 & 40 & 40 & 35 & 40 & 20 & 25 & 30 \
6 & 30 & 47 & 40 & 35 & 15 & 20 & 15 \
7 & 35 & 45 & 30 & 30 & 20 & 20 & 20 \
8 & 25 & 25 & 25 & 30 & 25 & 30 & 30 \
\hline
\end{array}$$ Assume the overall utility (sum of part-worths) of the current favorite Greenbell smartphone for customers 1 to 5 is 105 and customers 6 to 8 is 90. What new product design will maximize the share of choice for the eight consumers in the sample?

Accepted Answer

The answer of Greenbell Software Inc. conducted a study on...

Question 11

The worksheet formulation for integer linear programs and linear programming problems is exactly the same except that the _____ for integer linear programs.

Accepted Answer

A)  objective function using Set Objective in the Solver Parameters dialog box is set to Value Of option
B)  decision variables need not be added in By Changing Variable Cells in the Solver Parameters dialog box
C)  decision variables must be added in By Changing Variable Cells in the Solver Parameters dialog box along with selecting the Ignore Integer Constraints in the Integer Options dialog box
D)  constraints must be added in the Solver Parameters dialog box to identify the integer variables and the value for Tolerance in the Integer Options dialog box may need to be adjusted

Question 12

Coming up with a product design that will have the highest utility for a sufficient number of people to ensure sufficient sales to justify making the product is known as the ___________ in marketing literature.

Accepted Answer

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

Question 13

_____________ is a market research technique that can be used to learn how prospective buyers of a product value the product's attributes.

Accepted Answer

A)  Part-worth analysis
B)  Conjoint analysis
C)  Regression analysis
D)  Sensitivity analysis

Question 14

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.

Question 15

The results of _____________ can be used in an integer programming model of a product design and market share optimization problem.

Accepted Answer

A)  conjoint analysis
B)  product design
C)  part-worth
D)  variations analysis

Question 16

The objective function for a linear optimization problem is: Max 3x + 5y, with constraints x ≥ 0, y ≥ 0 and x and y are both integers and they are also 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.

Question 17

Delisshious Toasty Chocolates Company primarily produces two types of chocolate bars, Almond Tasty and Cashew Crunchy. The personnel costs incurred per day to produce the two types of chocolate bars are $100 and $120, respectively. The production cost per chocolate bar is $2 for Almond Tasty and $2.5 for Cashew Crunchy. The daily production capacity of Almond Tasty and Cashew Crunchy chocolate bars are 1100 and 1250, respectively. Only one type of bar can be produced on a given day since only one machine is available. Let C₁ = the number of Almond Tasty chocolate bars produced C₂ = the number of Cashew Crunchy chocolate bars are produced Y₁ = 1 if the machine produces Almond Tasty; 0, otherwise Y₂ = 1 if the machine produces Cashew Crunchy; 0, otherwise a. Write a constraint that sets the next day's maximum production of Almond Tasty to 1100. b. Write a constraint that sets the next day's maximum production of Cashew Crunchy to 1250. c. Write a constraint that requires that production be set up for exactly one of the two chocolates bars. d. Write the cost function to be minimized.

Accepted Answer

The answer of Delisshious Toasty Chocolates Company primarily produces two...

Question 18

In binary integer linear program, the integer variables take only the values

Accepted Answer

A)  0 or 1.
B)  0 or 8.
C)  1 or 8.
D)  1 or -1.

Question 19

The ___________ approach to solving integer linear optimization problems breaks the feasible region of the LP Relaxation into subregions until the subregions have integer solutions or it is determined that the solution cannot be in the subregion.

Accepted Answer

A)  cutting plane
B)  trial-and-error
C)  breaking region
D)  branch-and-bound

Question 20

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

Accepted Answer

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

Exam 12: Integer Linear Optimization Models

For a location problem, if the variables are defined as x_i = 1 if an outlet store is established in region i and 0 otherwise, the objective function is best defined by __________ for i = 1, 2, …, n number of outlet stores included in the problem.