integer linear programming

Project Description:

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($)

businesscalculus new 20000

finitemathematics revision 30000

general statistics new 15000

mathematicalstaistics new 10000

business statistics revision 25000

finance new 18000

financial accounting new 25000

managerialaccounting 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

businesscalculus 30 40 x

finitemathematics 16 24 x

general statistics 24 x 20

mathematicalstatistics 20 x 24

business statistics 10 x 16

finance x x 14

financial accounting x 24 26

managerialaccounting 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.

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.
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