Question 1

An integrality condition indicates that some (or all) of the

Accepted Answer

A) RHS values for constraints must be integer 
B) objective function coefficients must be integer 
C) constraint coefficients must be integer 
D) decision variables must be integer 
A) RHS values for constraints must be integer 
B) objective function coefficients must be integer 
C) constraint coefficients must be integer 
D) decision variables must be integer

Question 2

A company wants to build a new factory in either Atlanta or Columbia. It is also considering building a warehouse in whichever city is selected for the new factory. The following table shows the net present value (NPV) and cost of each facility. The company wants to maximize the net present value of its facilities, but it only has $16 million to invest.
   Based on this ILP formulation of the problem what is the optimal solution to the problem?

Accepted Answer

The answer of A company wants to build a new...

Question 3

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time. The city is divided into 4 zones. The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2. The number of tall buildings in each zone and the travel time between zones is listed below.
   Based on this ILP formulation of the problem what formulas should go in cells B13:B16, B20:E20, F20, and F23:F24 of the following Excel spreadsheet?
Let Xi = 1 if truck located in zone i, 0 otherwise

Accepted Answer

Question 4

Which of the following is not a benefit of using binary variables?

Accepted Answer

A) With only 2 values, Solver can work faster. 
B) Binary variables are useful in selection problems. 
C) Binary variables can replace some IF() conditions. 
D) Binary variables can enforce logical conditions. 
A) With only 2 values, Solver can work faster. 
B) Binary variables are useful in selection problems. 
C) Binary variables can replace some IF() conditions. 
D) Binary variables can enforce logical conditions.

Question 5

What are binary integer variables?

Accepted Answer

A) Variables with any two values, a and b 
B) Variables with values 0 and 1. 
C) Variables whose sum of digits is 2. 
D) Variables with values between 0 and 1. 
A) Variables with any two values, a and b 
B) Variables with values 0 and 1. 
C) Variables whose sum of digits is 2. 
D) Variables with values between 0 and 1.

Question 6

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.  
 The decision variables are defined as
Xi = the amount of product i produced
Yi = 1 if Xi > 0 and 0 if Xi = 0
Which of the following constraints creates the link between setting up to produce A's and making some A's for this problem?

Accepted Answer

A) X1 $\le$16Y1 
B) X1 -Y1 = 0 
C) X1 -18Y1 > 0 
D) = if(X1 > 0, Y1 = 1, Y1 = 0) 
A) X1 $\le$16Y1 
B) X1 -Y1 = 0 
C) X1 -18Y1 > 0 
D) = if(X1 > 0, Y1 = 1, Y1 = 0)

Question 7

A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?

Accepted Answer

A) X1 + X2 + X3 + X4 = 1 
B) X1 + X2 + X3 + X4 $\le$ 1 
C) X1 + X2 + X3 + X4 $\ge$1 
D) X1 + X2 + X3 + X4 $\ge$ 0 
A) X1 + X2 + X3 + X4 = 1 
B) X1 + X2 + X3 + X4 $\le$ 1 
C) X1 + X2 + X3 + X4 $\ge$1 
D) X1 + X2 + X3 + X4 $\ge$ 0

Question 8

A company needs to hire workers to cover a 7 day work week. Employees work 5 consecutive days with 2 days off. The demand for workers by day of the week and the wages per shift are:
   Formulate the ILP for this problem.

Accepted Answer

The answer of A company needs to hire workers to...

Question 9

A production company wants to ensure that if Product 1 is produced, production of Product 1 not exceed production of Product 2. Which of the following constraints enforce this condition?

Accepted Answer

A) X1 $\ge$ M2Y2 
B) X1 $\le$M2X2 
C) X1$\le$M1Y1, X1 $\le$Y1X2 
D) X1 $\le$X2 
A) X1 $\ge$ M2Y2 
B) X1 $\le$M2X2 
C) X1$\le$M1Y1, X1 $\le$Y1X2 
D) X1 $\le$X2

Question 10

An investor has $500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. The profit after one year, the cost and the number of units available are shown below.
   Based on this ILP formulation of the problem and the indicated optimal integer solution values what values should go in cells B5:F12 of the following Excel spreadsheet?

Accepted Answer

The answer of An investor has $500,000 to invest and...

Question 11

A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1's. It must produce more than 60 X2's for the X2 discount and 70 X3's for the X3 discount. How many decision variables are required in the formulation of this problem?

Accepted Answer

A) 3 
B) 6 
C) 9 
D) 12 
A) 3 
B) 6 
C) 9 
D) 12

Question 12

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time. The city is divided into 4 zones. The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2. The number of tall buildings in each zone and the travel time between zones is listed below.
Formulate the ILP for this problem.

Accepted Answer

The answer of A city wants to locate 2 new...

Question 13

Any integer variable in an ILP that assumes a fractional value in the optimal solution to the relaxed LP problem can be designated

Accepted Answer

A) a diverging variable. 
B) a branching variable. 
C) a bifurcating variable. 
D) a splitting variable. 
A) a diverging variable. 
B) a branching variable. 
C) a bifurcating variable. 
D) a splitting variable.

An integrality condition indicates that some (or all) of the

Which of the following is not a benefit of using binary variables?

What are binary integer variables?

A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?

A company needs to hire workers to cover a 7 day work week. Employees work 5 consecutive days with 2 days off. The demand for workers by day of the week and the wages per shift are: Formulate the ILP for this problem.

A production company wants to ensure that if Product 1 is produced, production of Product 1 not exceed production of Product 2. Which of the following constraints enforce this condition?

Any integer variable in an ILP that assumes a fractional value in the optimal solution to the relaxed LP problem can be designated

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

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Exam 6: Integer Linear Programming

An integrality condition indicates that some (or all) of the

Which of the following is not a benefit of using binary variables?

What are binary integer variables?

A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?

A company needs to hire workers to cover a 7 day work week. Employees work 5 consecutive days with 2 days off. The demand for workers by day of the week and the wages per shift are: Formulate the ILP for this problem.

A production company wants to ensure that if Product 1 is produced, production of Product 1 not exceed production of Product 2. Which of the following constraints enforce this condition?

Any integer variable in an ILP that assumes a fractional value in the optimal solution to the relaxed LP problem can be designated

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters