Question 1

Sansuit Investments is deciding on future investment for the coming two years. The company considered four bonds to choose from and their investment details for the next two years are given in the table below:
  
The net worth of these four bonds is $75,000, $40,000, $25,500, and $18,000, respectively. The funds available with the company for Year 1 and Year 2 are $35,000 and $62,000, respectively. a. Develop and solve a binary integer programming model for maximizing the net worth assuming that only one of the bonds can be considered.
b. Suppose the investment has to be made on Bond B, and only two of the four bonds can be considered for investment. Modify your formulation from part a. to reflect this new situation. Of these two options, which is better?

Accepted Answer

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Question 2

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) provided with the phone. Eight sample customers have participated in the study and provided the following part-worths for each of the above attributes.
  
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

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Question 3

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

The answer of A coffee maker vendor has set up...

Question 4

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

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Question 5

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

The answer of A manufacturer makes two types of rubber,...

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

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Question 7

BBest Ink Printing Co. received an order to print a minimum of 50,000 tickets for a concert. They have three printing machines available to meet the order they received. The set-up cost of these machines and the unit cost/ticket printed using each machine along with their maximum production are provided in the table below:
  a. Formulate a binary integer linear programming model to find two machines that could be used to print the required number of tickets in order to minimize the cost.
b. Solve the problem in part a.

Accepted Answer

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Question 8

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

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Question 9

A manufacturer wants to construct warehouses in six different locations of the city to supply dry cells to his customers on time. The manufacturer wants to construct the minimum number of warehouses, to meet the market demand on time, such that at least one warehouse is within 40 miles from each other warehouse. The following table provides the distance (in miles) between the locations.
  
Formulate and solve an integer linear program that can be used to determine the minimum number of warehouses needed to be constructed. What are their locations?

Accepted Answer

The answer of A manufacturer wants to construct warehouses 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) provided with the phone. Eight sample customers have participated in the study and provided the following part-worths for each of the above attributes.
  
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

Light-Twilight Inc. currently has four workshops for manufacturing light bulbs and five warehouses where the produced light bulbs are shipped from the workshops for storage. The cost, demand, and volume details are given as below:
  a. Formulate a mixed-integer programming model to identify two workshops the management should retain in order to fulfil the estimated demand that minimizes the cost.
b. Solve the model you formulated in part a. What is the optimum cost?

Accepted Answer

The answer of Light-Twilight Inc. currently has four workshops for...

Question 12

ROFiL Pizza Delivery is planning to open new stores in different other regions so that the excess demand for the pizza home delivery services is met. The locations under consideration and the potential areas (coded in numbers 1-9) that can be reached quickly from the considered locations for home delivery are given in the following table:
  
Formulate an integer programming model that could be used to find the minimum number of stores to open in order to cover customers of all areas for the home delivery service.

Accepted Answer

The answer of ROFiL Pizza Delivery is planning to open...

Question 13

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

The answer of A manufacturer makes two types of rubber,...

Question 14

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

The answer of A coffee manufacturing company has two different...

Question 15

ROFiL Pizza Delivery is planning to open new stores in different other regions so that the excess demand for the pizza home delivery services is met. The locations under consideration and the potential areas (coded in numbers 1-9) that can be reached quickly from the considered locations for home delivery are given in the following table:
  
Solve an integer programming model that could be used to find the minimum number of stores to open in order to cover customers of all areas for the home delivery service.

Accepted Answer

The answer of ROFiL Pizza Delivery is planning to open...

Question 16

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

The answer of A chocolate making company largely produces one...

Question 17

Delisshious Toasty Chocolates Company largely produces two types of chocolate bars, Almond Tasty and Cashew Crunchy. The maintenance costs per day incurred to produce the two types of chocolate bars are $100 and $120, respectively. The manufacturing 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. There is only one machine to produce whichever type of chocolate bar will be produced that day. Only one type of bar can be made on a given day.
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

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Question 18

FinFone Paper Mill is a small-scale paper making company which has four making machines to produce four different types of papers. Each type of paper must go through processing on each of four machines. The manufacturing time (in minutes) per unit of paper produced is in the following table:
  
The maximum time allotted for each machine is 30 hours per week and at least 100 units of each type of paper should be made using these machines during the week.
Profit per unit is:
  
Develop and solve an all-integer model that will determine, using the available machine time, the number of units of each paper type to be produced in order to meet the weekly demand and to maximize the profit.

Accepted Answer

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Question 19

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.
-One stock can have a maximum invest 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 chosen should be two.
-The total amount invested in Banking must be at least as much as the amount invested in Agriculture.
Now, 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 20

Sansuit Investments is deciding on future investment for the coming two years. The company considered four bonds to choose from and their investment details for the next two years are given in the table below:
  
The net worth of these four bonds is $75,000, $40,000, $25,500, and $18,000, respectively. The funds available with the company for Year 1 and Year 2 are $35,000 and $62,000, respectively. Develop and solve a binary integer programming model for maximizing the net worth.

Accepted Answer

The answer of Sansuit Investments is deciding on future investment...

Quiz 9: Integer Linear Optimization Models