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Exam 9: Integer Linear Optimization Models

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Question 21

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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?

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Note: There are alternative optima for t...

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Question 22

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

A) all-integer linear program
B) mixed-integer linear program
C) LP relaxation of the integer linear program
D) binary integer linear program

E) A) and D)
F) A) and B)

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Question 23

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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.

Which of the following is true of the relationship between the value of the optimal integer solution and the value of the optimal solution to the LP Relaxation?

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.

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?

_____ is a constraint requiring that two binary variables be equal and that thus are both either in or out of the solution together.

The imposition of integer restriction is necessary for models where:

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.

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.

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?

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 _____.

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.

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

The linear program that results from dropping the integer requirements for the variables in an integer linear program is known as _____.

In a fixed-cost model, each fixed cost is associated with a binary variable and a specification of the:

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.

Reference - 9.1. What category does the above objective fall under?

The _____ of a set of points is the smallest intersection of linear inequalities that contain the set of points.

In a production application involving a fixed cost and a variable cost, the use of _____ makes including the fixed cost possible in a production model.