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Integer Linear Regression

ASW Publishing Inc., a small publisher of 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 (1000's)
Business Calculus New 20
Finite Math Revision 30
General Statistics New 15
Mathematical Statistics New 10
Business Statistics Revision 25
Finance New 18
Financial Accounting New 25
Managerial Accounting Revision 50
English Literature New 20
German New 30

The books listed as revisions are texts that ASW already has under contract; these texts are being considered for publications as new editions. The books that are listed as new have been reviewed by the company, but contract have not yet been signed.
Three individuals in the company can be assigned 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 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.

Book Subject John Susan Monica
Business Calculus 30 40 X
Finite Math 16 24 X
General Statistics 24 X 30
Math 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

ASW will not publish more than two statistics books or more than one accounting text in a single year. In addition, management decided that one of the mathematics textbooks (business calculus or finite math) must be published, but not both.

Managerial Report
Prepare a report for the managing editor of ASW that describes your findings and recommendations regarding the best publication strategy for next year. In carrying out your analysis, assume that the fixed costs and sales revenue per unit are approximately equal for all books; management is interested primarily in maximizing total unit sales volume. The managing editor also asked that you include recommendations regarding the following possible changes.
1. If it would be advantageous to do so, Susan can be moved off another project to allow her to work 12 more days.
2. If it would be advantageous to do so, Monica can also be made available for another 10 days.
3. 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.
Formulate a integer linear program, use Lindo to determine optimal levels and provide an analysis.

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Solution Summary

ASW Publishing Inc., a small publisher of 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 (1000's)
Business Calculus New 20
Finite Math Revision 30
General Statistics New 15
Mathematical Statistics New 10
Business Statistics Revision 25
Finance New 18
Financial Accounting New 25
Managerial Accounting Revision 50
English Literature New 20
German New 30

The books listed as revisions are texts that ASW already has under contract; these texts are being considered for publications as new editions. The books that are listed as new have been reviewed by the company, but contract have not yet been signed.
Three individuals in the company can be assigned 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 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.

Book Subject John Susan Monica
Business Calculus 30 40 X
Finite Math 16 24 X
General Statistics 24 X 30
Math 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

ASW will not publish more than two statistics books or more than one accounting text in a single year. In addition, management decided that one of the mathematics textbooks (business calculus or finite math) must be published, but not both.

Managerial Report
Prepare a report for the managing editor of ASW that describes your findings and recommendations regarding the best publication strategy for next year. In carrying out your analysis, assume that the fixed costs and sales revenue per unit are approximately equal for all books; management is interested primarily in maximizing total unit sales volume. The managing editor also asked that you include recommendations regarding the following possible changes.
1. If it would be advantageous to do so, Susan can be moved off another project to allow her to work 12 more days.
2. If it would be advantageous to do so, Monica can also be made available for another 10 days.
3. 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.
Formulate a integer linear program, use Lindo to determine optimal levels and provide an analysis.

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