Assuming W1, W2 and W3 are 0 -1 integer variables, the constraint W1 + W2 + W3 < 1 is often called a

A) multiple-choice constraint. B) mutually exclusive constraint. C) k out of n alternatives constraint. D) corequisite constraint. A) multiple-choice constraint. B) mutually exclusive constraint. C) k out of n alternatives constraint. D) corequisite constraint.

Exam 7: Integer Linear Programming

Your express package courier company is drawing up new zones for the location of drop boxes for customers. The city has been divided into the seven zones shown below. You have targeted six possible locations for drop boxes. The list of which drop boxes could be reached easily from each zone is listed below. Let x_i = 1 if drop box location i is used, 0 otherwise. Develop a model to provide the smallest number of locations yet make sure that each zone is covered by at least two boxes.

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Question 21

The solution to the LP Relaxation of a maximization integer linear program provides

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Question 22

Given the following all-integer linear program: Max 15x₁ + 2x₂ s. t. 7x₁ + x₂ < 23 3x₁ - x₂ < 5 x₁, x₂ > 0 and integer a. Solve the problem as an LP, ignoring the integer constraints. b. What solution is obtained by rounding up fractions greater than or equal to 1/2? Is this the optimal integer solution? c. What solution is obtained by rounding down all fractions? Is this the optimal integer solution? Explain. d. Show that the optimal objective function value for the ILP is lower than that for the optimal LP. e. Why is the optimal objective function value for the ILP problem always less than or equal to the corresponding LP's optimal objective function value? When would they be equal? Comment on the MILP's optimal objective function compared to the corresponding LP & ILP.

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Question 23

Most practical applications of integer linear programming involve

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Question 24

Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

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Question 25

Let x₁ , x₂ , and x₃ be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?

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Question 26

The Westfall Company has a contract to produce 10,000 garden hoses for a large discount chain. Westfall has four 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. a.This problem requires two different kinds of decision variables. Clearly define each kind. b.The company wants to minimize total cost. Give the objective function. c.Give the constraints for the problem. d.Write a constraint to ensure that if machine 4 is used, machine 1 cannot be.

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Question 27

The use of integer variables creates additional restrictions but provides additional flexibility. Explain.

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Question 28

A business manager for a grain distributor is asked to decide how many containers of each of two grains to purchase to fill its 1,600 pound capacity warehouse. The table below summarizes the container size, availability, and expected profit per container upon distribution. $A business manager for a grain distributor is asked to decide how many containers of each of two grains to purchase to fill its 1,600 pound capacity warehouse. The table below summarizes the container size, availability, and expected profit per container upon distribution. a. Formulate as a linear program with the decision variables representing the number of containers purchased of each grain. Solve for the optimal solution. b. What would be the optimal solution if you were not allowed to purchase fractional containers? c. There are three possible results from rounding an LP solution to obtain an integer solution: (1) the rounded optimal LP solution will be the optimal IP solution; (2) the rounded optimal LP solution gives a feasible, but not optimal IP solution; (3) the rounded optimal LP solution is an infeasible IP solution. For this problem (i) round down all fractions; (ii) round up all fractions; (iii) round off (to the nearest integer) all fractions (NOTE: Two of these are equivalent.) Which result above (1, 2, or 3) occurred under each rounding method?$ a. Formulate as a linear program with the decision variables representing the number of containers purchased of each grain. Solve for the optimal solution. b. What would be the optimal solution if you were not allowed to purchase fractional containers? c. There are three possible results from rounding an LP solution to obtain an integer solution: (1) the rounded optimal LP solution will be the optimal IP solution; (2) the rounded optimal LP solution gives a feasible, but not optimal IP solution; (3) the rounded optimal LP solution is an infeasible IP solution. For this problem (i) round down all fractions; (ii) round up all fractions; (iii) round off (to the nearest integer) all fractions (NOTE: Two of these are equivalent.) Which result above (1, 2, or 3) occurred under each rounding method?

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Question 29

The constraint x₁ − x₂ = 0 implies that if project 1 is selected, project 2 cannot be.

(True/False)

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Question 30

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

(True/False)

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Question 31

Give a verbal interpretation of each of these constraints in the context of a capital budgeting problem. a. x1 − x2 ≥ 0 b. x1 − x2 = 0 c. x1 + x2 + x3 ≤ 2

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Question 32

The 0-1 variables in the fixed cost models correspond to

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Question 33

Explain how integer and 0-1 variables can be used in an objective function to minimize the sum of fixed and variable costs for production on two machines.

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Question 34

Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.

(True/False)

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Question 35

Rounding the solution of an LP Relaxation to the nearest integer values provides

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Question 36

Assuming W₁, W₂ and W₃ are 0 -1 integer variables, the constraint W₁ + W₂ + W₃ < 1 is often called a

(Multiple Choice)

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Question 37

The constraint x₁ + x₂ + x₃ + x₄ ≤ 2 means that two out of the first four projects must be selected.

(True/False)

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Question 38

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

(True/False)

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Question 39

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

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Question 40

Showing 21 - 40 of 61

The solution to the LP Relaxation of a maximization integer linear program provides

Most practical applications of integer linear programming involve

Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

Let x₁ , x₂ , and x₃ be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?

The use of integer variables creates additional restrictions but provides additional flexibility. Explain.

The constraint x₁ − x₂ = 0 implies that if project 1 is selected, project 2 cannot be.

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

Give a verbal interpretation of each of these constraints in the context of a capital budgeting problem. a. x1 − x2 ≥ 0 b. x1 − x2 = 0 c. x1 + x2 + x3 ≤ 2

The 0-1 variables in the fixed cost models correspond to

Explain how integer and 0-1 variables can be used in an objective function to minimize the sum of fixed and variable costs for production on two machines.

Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.

Rounding the solution of an LP Relaxation to the nearest integer values provides

Assuming W₁, W₂ and W₃ are 0 -1 integer variables, the constraint W₁ + W₂ + W₃ < 1 is often called a

The constraint x₁ + x₂ + x₃ + x₄ ≤ 2 means that two out of the first four projects must be selected.

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 7: Integer Linear Programming

The solution to the LP Relaxation of a maximization integer linear program provides

Most practical applications of integer linear programming involve

​Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?

​The use of integer variables creates additional restrictions but provides additional flexibility. Explain.

The constraint x1 − x2 = 0 implies that if project 1 is selected, project 2 cannot be.

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

​Give a verbal interpretation of each of these constraints in the context of a capital budgeting problem. a. x1 − x2 ≥ 0 b. x1 − x2 = 0 c. x1 + x2 + x3 ≤ 2

The 0-1 variables in the fixed cost models correspond to

​Explain how integer and 0-1 variables can be used in an objective function to minimize the sum of fixed and variable costs for production on two machines.

Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.

Rounding the solution of an LP Relaxation to the nearest integer values provides

​Assuming W1, W2 and W3 are 0 -1 integer variables, the constraint W1 + W2 + W3 < 1 is often called a

The constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

Let x₁ , x₂ , and x₃ be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?

The use of integer variables creates additional restrictions but provides additional flexibility. Explain.

The constraint x₁ − x₂ = 0 implies that if project 1 is selected, project 2 cannot be.

Give a verbal interpretation of each of these constraints in the context of a capital budgeting problem. a. x1 − x2 ≥ 0 b. x1 − x2 = 0 c. x1 + x2 + x3 ≤ 2

Explain how integer and 0-1 variables can be used in an objective function to minimize the sum of fixed and variable costs for production on two machines.

Assuming W₁, W₂ and W₃ are 0 -1 integer variables, the constraint W₁ + W₂ + W₃ < 1 is often called a

The constraint x₁ + x₂ + x₃ + x₄ ≤ 2 means that two out of the first four projects must be selected.