Question 1

In a linear model,the target cell and constraints are ultimately:

Accepted Answer

A)  a product of changing cells 
B)  a sum of products of changing cells 
C)  a product of constants and changing cells 
D)  a sum of products of constants and changing cells 
A)  a product of changing cells 
B)  a sum of products of changing cells 
C)  a product of constants and changing cells 
D)  a sum of products of constants and changing cells D

Question 2

Exhibit 6-2
Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The variable unit cost of shipping a ton is $1 per mile. The number of miles between the respective plants is shown in the table below:
In addition to the variable unit costs of shipping, Sinclair incurs a fixed handling cost (of pickup and delivery) for any shipping routes it uses. These costs are discounted for longer routes, as shown below:
 $$\begin{array} { | l | l | l | l | } 
\hline & \text { Grand Rapids } & \text { Blue Ridge } & \text { Sunset } \
\hline \text { Ohio Valley } & 50 & 40 & 100 \
\hline \text { Lakeview } & 60 & 50 & 75 \
\hline
\end{array}$$ 
$\begin{array}{c}
\text { Fixed Cost Levels }\
\begin{array}{lll}
\text { Distance (mi)}&\text { Fixed Cost } \
<=25 & \$ 100,000 \
<=50 & \$ 60,000 \
<=75 & \$ 20,000 \
<=100 & \$ 0
\end{array}

\end{array}$

-Refer to Exhibit 6-2.Suppose the shipping capacity for all routes is 3000 tons per month.What is Sinclair's optimal shipping plan in that case
 What is the total cost in that case

Accepted Answer

The solved model is shown below.Sinclair will be forced to use all but the Lakeview to Grand Rapids route,which increases the total cost substantially to $895,000.​

Question 3

Exhibit 6-2
Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The variable unit cost of shipping a ton is $1 per mile. The number of miles between the respective plants is shown in the table below:
In addition to the variable unit costs of shipping, Sinclair incurs a fixed handling cost (of pickup and delivery) for any shipping routes it uses. These costs are discounted for longer routes, as shown below:
 $$\begin{array} { | l | l | l | l | } 
\hline & \text { Grand Rapids } & \text { Blue Ridge } & \text { Sunset } \
\hline \text { Ohio Valley } & 50 & 40 & 100 \
\hline \text { Lakeview } & 60 & 50 & 75 \
\hline
\end{array}$$ 
$\begin{array}{c}
\text { Fixed Cost Levels }\
\begin{array}{lll}
\text { Distance (mi)}&\text { Fixed Cost } \
<=25 & \$ 100,000 \
<=50 & \$ 60,000 \
<=75 & \$ 20,000 \
<=100 & \$ 0
\end{array}

\end{array}$

-Refer to Exhibit 6-2.What is Sinclair's optimal shipping plan
 What is the total cost in that case

Accepted Answer

The solved model is shown below.Sinclair will ship from Ohio Valley to Blue Ridge,and from Lakeview to Grand Rapids and Sunset.The total cost is $780,000.​

Question 4

The default integer optimality setting in Solver is:

Accepted Answer

A)  0.1% 
B)  0.5% 
C)  1% 
D)  5% 
A)  0.1% 
B)  0.5% 
C)  1% 
D)  5%

Question 5

Rounding the solution of a linear programming to the nearest integer values provides an:

Accepted Answer

A)  integer solution that is optimal 
B)  integer solution that is not optimal 
C)  integer solution that might be optimal 
D)  infeasible solution 
A)  integer solution that is optimal 
B)  integer solution that is not optimal 
C)  integer solution that might be optimal 
D)  infeasible solution

Question 6

In a model with 8 changing cells,all of which are constrained to be binary,the number of potentially feasible solutions is:

Accepted Answer

A)  4 
B)  8 
C)  64 
D)  256 
A)  4 
B)  8 
C)  64 
D)  256

Question 7

The LP relaxation of an integer programming (IP)problem is typically easy to solve and provides a bound for the IP model.

Accepted Answer

A) True 
 B)False

Question 8

In a set-covering model,each member of a given set (set 1)must be "covered" by all members of another set (set 2).

Accepted Answer

A) True 
 B)False

Question 9

Optimization software,including Solver,typically has more difficulty solving an integer programming problem,relative to a linear programming problem.

Accepted Answer

A) True 
 B)False

Question 10

Exhibit 6-1
A recent college graduate is planning to move cross country from her college town to the city where her first job is located. She has rented a truck that can haul up to 1100 cubic feet of furniture. The volume and value of each item she is considering moving on the truck are given below.
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & \text { Bedroom Set } & \text { Dining Set } & \text { Stereo } & \text { Sofa } & \text { TV } \
\hline \text { Value } & \$ 450 & \$ 500 & \$ 150 & \$ 200 & \$ 100 \
\hline \text { Volume } & 800 & 600 & 300 & 400 & 80 \
\hline
\end{array}$$
-Refer to Exhibit 6-1.This problem is an example of what type of integer programming model

Accepted Answer

This is an integer programming model req

Question 11

If Solver fails to find an optimal solution to an integer programming problem,we might be able to find a near optimal solution by specifying a smaller number for the integer optimality setting.

Accepted Answer

A) True 
 B)False

Question 12

An algorithm which uses implicit enumeration:

Accepted Answer

A)  is impractical 
B)  examines all possible solutions 
C)  does not guarantee that some of the solutions not examined could be optimal 
D)  excludes many possible solutions that guaranteed to be suboptimal 
A)  is impractical 
B)  examines all possible solutions 
C)  does not guarantee that some of the solutions not examined could be optimal 
D)  excludes many possible solutions that guaranteed to be suboptimal

Question 13

Exhibit 6-1
A recent college graduate is planning to move cross country from her college town to the city where her first job is located. She has rented a truck that can haul up to 1100 cubic feet of furniture. The volume and value of each item she is considering moving on the truck are given below.
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & \text { Bedroom Set } & \text { Dining Set } & \text { Stereo } & \text { Sofa } & \text { TV } \
\hline \text { Value } & \$ 450 & \$ 500 & \$ 150 & \$ 200 & \$ 100 \
\hline \text { Volume } & 800 & 600 & 300 & 400 & 80 \
\hline
\end{array}$$
-Refer to Exhibit 6-1.Suppose she can save $400 by renting a smaller truck,which has only 800 cubic feed of capacity.Would she be better off with the smaller truck

Accepted Answer

The revised knapsack model is shown belo

Question 14

The branch and bound algorithm uses:

Accepted Answer

A)  lower bounds 
B)  upper bounds 
C)  both upper and lower bounds 
D)  neither upper or lower bounds 
A)  lower bounds 
B)  upper bounds 
C)  both upper and lower bounds 
D)  neither upper or lower bounds

Question 15

Many inherently nonlinear problems can be transformed into linear models with the use of:

Accepted Answer

A)  integer variables 
B)  integer constraints 
C)  binary variables 
D)  binary constraints 
A)  integer variables 
B)  integer constraints 
C)  binary variables 
D)  binary constraints

Question 16

During the solution of a maximization problem with the branch and bound algorithm,an incumbent solution represents an upper bound on the solution.

Accepted Answer

A) True 
 B)False

Question 17

Fixed costs imply that the divisibility assumption of linear models no longer holds.

Accepted Answer

A) True 
 B)False

Question 18

Exhibit 6-1
A recent college graduate is planning to move cross country from her college town to the city where her first job is located. She has rented a truck that can haul up to 1100 cubic feet of furniture. The volume and value of each item she is considering moving on the truck are given below.
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & \text { Bedroom Set } & \text { Dining Set } & \text { Stereo } & \text { Sofa } & \text { TV } \
\hline \text { Value } & \$ 450 & \$ 500 & \$ 150 & \$ 200 & \$ 100 \
\hline \text { Volume } & 800 & 600 & 300 & 400 & 80 \
\hline
\end{array}$$
-Refer to Exhibit 6-1.Which items should she take with her to her new home
 What is the value of these items

Accepted Answer

The solved knapsack model is s

Question 19

The higher the upper bound produced for a maximization problem in the branch and bound solution process,the faster the algorithm will be.

Accepted Answer

A) True 
 B)False

Question 20

Exhibit 6-3
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection):
  
-Refer to Exhibit 6-3.Suppose PharmaCo wants to have a backup for each city.What is the minimum number of representatives that can cover this region in that case
 What are their home cities

Accepted Answer

PharmaCo would need to deploy

In a linear model,the target cell and constraints are ultimately:

The default integer optimality setting in Solver is:

Rounding the solution of a linear programming to the nearest integer values provides an:

In a model with 8 changing cells,all of which are constrained to be binary,the number of potentially feasible solutions is:

The LP relaxation of an integer programming (IP)problem is typically easy to solve and provides a bound for the IP model.

In a set-covering model,each member of a given set (set 1)must be "covered" by all members of another set (set 2).

Optimization software,including Solver,typically has more difficulty solving an integer programming problem,relative to a linear programming problem.

If Solver fails to find an optimal solution to an integer programming problem,we might be able to find a near optimal solution by specifying a smaller number for the integer optimality setting.

An algorithm which uses implicit enumeration:

The branch and bound algorithm uses:

Many inherently nonlinear problems can be transformed into linear models with the use of:

During the solution of a maximization problem with the branch and bound algorithm,an incumbent solution represents an upper bound on the solution.

Fixed costs imply that the divisibility assumption of linear models no longer holds.

The higher the upper bound produced for a maximization problem in the branch and bound solution process,the faster the algorithm will be.

Introduction to Modeling

Introduction to Spreadsheet Modeling

Introduction to Optimization Modeling

Linear Programming Models

Network Models

Nonlinear Optimization Models

Evolutionary Solver: An Alternative Optimization Procedure

Decision Making Under Uncertainty

Introduction to Simulation Modeling

Simulation Models

Queueing Models

Regression and Forecasting Models

Data Mining

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Exam 6: Optimization Models With Integer Variables

In a linear model,the target cell and constraints are ultimately:

The default integer optimality setting in Solver is:

Rounding the solution of a linear programming to the nearest integer values provides an:

In a model with 8 changing cells,all of which are constrained to be binary,the number of potentially feasible solutions is:

The LP relaxation of an integer programming (IP)problem is typically easy to solve and provides a bound for the IP model.

In a set-covering model,each member of a given set (set 1)must be "covered" by all members of another set (set 2).

Optimization software,including Solver,typically has more difficulty solving an integer programming problem,relative to a linear programming problem.

If Solver fails to find an optimal solution to an integer programming problem,we might be able to find a near optimal solution by specifying a smaller number for the integer optimality setting.

An algorithm which uses implicit enumeration:

The branch and bound algorithm uses:

Many inherently nonlinear problems can be transformed into linear models with the use of:

During the solution of a maximization problem with the branch and bound algorithm,an incumbent solution represents an upper bound on the solution.

Fixed costs imply that the divisibility assumption of linear models no longer holds.

The higher the upper bound produced for a maximization problem in the branch and bound solution process,the faster the algorithm will be.

Introduction to Modeling

Introduction to Spreadsheet Modeling

Introduction to Optimization Modeling

Linear Programming Models

Network Models

Nonlinear Optimization Models

Evolutionary Solver: An Alternative Optimization Procedure

Decision Making Under Uncertainty

Introduction to Simulation Modeling

Simulation Models

Queueing Models

Regression and Forecasting Models

Data Mining

Filters