ASW Publishing, Inc. a small publisher of college textbooks,must make a decision
ID: 2958191 • Letter: A
Question
ASW Publishing, Inc. a small publisher of college textbooks,must make a decision regarding which books to publish next year. The books under consideration are listed in the following table, along with the projected three-year sales expected from each book:
Book Subject Type of Book Projected Sales($)
Business Calculus New 20000
Finite Mathematics Revision 30000
General Statistics New 15000
Mathematical Statistics New 10000
Business Statistics Revision 25000
Finance New 18000
Financial Accounting New 25000
Managerial Accounting Revision 50000
English Literature New 20000
German New 30000
The books listed as revisions are texts that ASW already has under contract; these books are being considered for publication as new editions. The books that are listed as new have been reviewed by the company, but contracts have not yet been signed.
Three individuals in the company can be assigned to to these projects, all of whom have varying amounts of time available; John has 60 days available, and Susan and Monica both have 40 days available. The days required by each person to complete each project are shown in the following table. For instance, if the business calculus book is published, it will require 30 days of John's time and 40 days of Susan's time. An "X" indicates that the person will not be used on the project. Note that at least two staff members will be assigned to each project except the finance book.
ASW will not publish more than two statistics books or more than one accounting book in a single year. In addition, management decided that one of the mathematics books (business calculus or finite math) must be published, but not both.
Book Subject John Susan Monica
Business Calculus 30 40 X
Finite Mathematics 16 24 X
General Statistics 24 X 20
Mathematical Statistics 20 X 24
Business Statistics 10 X 16
Finance X X 14
Financial Accounting X 24 26
Managerial Accounting X 28 30
English Literature 40 34 30
German X 50 36
Prepare a report for the managing editor of ASW that describes your findings and recommendations regarding the best publication strategy for the next year. In carrying out your analysis, assume that the fixed costs and the sales revenue per unit are approximately equal for all books: management is interested primarily in maximizing the total unit sales volume.
I need a maximization integer linear model with constraints included.
The managing editor also asked that you include recommendations regarding the following possible changes:
If it would be advantageous to do so, Susan can be moved off another project to allow her to work 12 more days.
If it would be advantageous to do so, Monica can also be made available for another 10 days.
If one or more of the revisions could be postponed for another year, should they be? Clearly the company will risk losing market share by postponing a revision.
Explanation / Answer
Management Report
TO: ASW Publishing, Inc. Management
FROM: Your Name
DATE: Current Date
SUBJECT: Publication Strategy Analysis and Recommendations
Section of Report
Statement of the Business Problem.. 4
Other requirements. 4
Constraints Applied on Strategy. 4
Assumptions in analysis. 4
Decision Variables. 5
Analysis, Results and Recommendations. 6
Appendices. 10
Statement of the Business Problem
Other requirements
Constraints Applied on Strategy
Assumptions in analysis
Fixed costs and the sales revenue per unit are approximately equal for all books
Decision Variables
Here are the 0/1 decision variables.
Value
Book
Decision Variable
Not selected for publication
Selected for publication
Business Calculus
BusCalc
0
1
Finite Math text
FinMath
0
1
General Statistics text
GenStat
0
1
Mathematics Statistics text
MathStat
0
1
Business Statistics text
BusStat
0
1
Finance text
Finance
0
1
Financial Accounting text
FinAcct
0
1
Managerial Accounting text
ManAcct
0
1
English Literature text
EngLit
0
1
German text
German
0
1
Analysis, Results and Recommendations
Requirement Case One:
If it would be advantageous to do so, Susan can be moved off another project to allow her to work 12 more days.
Optimal Solution for this Requirement is provided as follows:
Constraints Applied: Please check Appendix A for constraints
Decisions For book publication
Object Function value: 73.000
Decision Variable
Value
BusCalc
0
FinMath
1
GenStat
0
MathStat
0
BusStat
1
Finance
1
FinAcct
0
ManAcct
0
EngLit
0
German
0
Slack Value obtained:
Constraint
Slack/Surplus
1
34
2
16
3
10
4
1
5
1
6
0
Findings:
Analysis and Recommendations:
Expected Sales are less. Thus this strategy is not advantageous
Result: This publication Strategy is not recommended
Requirement Case 2:
If it would be advantageous to do so, Monica can also be made available for another 10 days
Optimal Solution for this Requirement is provided as follows:
Constraints Applied: Please check Appendix B for constraints
Decisions For book publication
Object Function value: 80.000
Decision Variable
Value
BusCalc
0
FinMath
1
GenStat
0
MathStat
0
BusStat
0
Finance
0
FinAcct
0
ManAcct
1
EngLit
0
German
0
Slack Value obtained:
Constraint
Slack/Surplus
1
44
2
0
3
10
4
2
5
0
6
0
Findings:
Analysis and Recommendations:
Sales are more, but John is not used, therefore, this strategy is not advantageous.
Result: This publication Strategy is not recommended.
Optimal Solution to increase sales and make better use of all resources
Optimal Solution for this Requirement is provided as follows:
Constraints Applied: Please check Appendix C for constraints
Decisions For book publication
Object Function value: 105.000
Decision Variable
Value
BusCalc
0
FinMath
1
GenStat
0
MathStat
0
BusStat
1
Finance
0
FinAcct
0
ManAcct
1
EngLit
0
German
0
Slack Value obtained:
Constraint
Slack/Surplus
1
34
2
0
3
4
4
1
5
0
6
0
Findings:
Analysis and Recommendations:
Sales are more 105,000 books. Monica and Susan are now moved to other projects
Result: This publication Strategy is recommended.
Recommendations for Requirement Case 3:
Appendices
APPENDIX A:
Maximum Publications possible:
Book
Publishing numbers
Business Calculus
20
Finite Math text
30
General Statistics text
15
Mathematics Statistics text
10
Business Statistics text
25
Finance text
18
Financial Accounting text
25
Managerial Accounting text
50
English Literature text
20
German text
30
Requirement Case 1:
Constraint
/ Decision Variable
1
2
3
4
5
6
BusCalc
30
40
0
0
0
1
FinMath
16
24
0
0
0
1
GenStat
24
0
30
1
0
0
MathStat
20
0
24
1
0
0
BusStat
10
0
16
1
0
0
Finance
0
0
14
0
0
0
FinAcct
0
24
26
0
1
0
ManAcct
0
28
30
0
1
0
EngLit
40
34
30
0
0
0
German
0
50
36
0
0
0
<60
<40
<40
<2
<1
=1
APPENDIX B:
Maximum Publications possible:
Book
Publishing numbers
Business Calculus
20
Finite Math text
30
General Statistics text
15
Mathematics Statistics text
10
Business Statistics text
25
Finance text
18
Financial Accounting text
25
Managerial Accounting text
50
English Literature text
20
German text
30
Requirement Case 2:
Constraint
/ Decision Variable
1
2
3
4
5
6
BusCalc
30
40
0
0
0
1
FinMath
16
24
0
0
0
1
GenStat
24
0
30
1
0
0
MathStat
20
0
24
1
0
0
BusStat
10
0
16
1
0
0
Finance
0
0
14
0
0
0
FinAcct
0
24
26
0
1
0
ManAcct
0
28
30
0
1
0
EngLit
40
34
30
0
0
0
German
0
50
36
0
0
0
<60
<52
<40
<2
<1
=1
Value
Book
Decision Variable
Not selected for publication
Selected for publication
Business Calculus
BusCalc
0
1
Finite Math text
FinMath
0
1
General Statistics text
GenStat
0
1
Mathematics Statistics text
MathStat
0
1
Business Statistics text
BusStat
0
1
Finance text
Finance
0
1
Financial Accounting text
FinAcct
0
1
Managerial Accounting text
ManAcct
0
1
English Literature text
EngLit
0
1
German text
German
0
1