Question

Case Problem 1 TEXTBOOK PUBLISHING 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 Subject Business calculus Finite mathematics General statistics Mathematical statistics Business statistics Finance Financial accounting Managerial accounting English literature German Type of Book Projected Sales ($1000s) Revision 10 18 Revision New New The books listed as revisions are texts that ASW already has under contract: these texts 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 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. Monica John 30 Susan Book Subject Business calculus Finite mathematics General statistics Mathematical statistics Business statistics 16 14 24 Financial accounting Managerial accounting English literature 30 30 a single year. In addition, management decided that one of the mathematics books (business calculus or finite math) must be published, but not both. ASW will not publish more than two statistics books or more than one accounting text in

> What book is it? Do you know where I can find it? Is it accessible to the public?

Answer 1

Modeling

Decision variable:

X1= 1 if book business calculus is scheduled for publication

        0 otherwise

X2= 1 if book final math is scheduled for publication

        0 otherwise

X3= 1 if book general statistics is scheduled for publication

        0 otherwise

X4=1 if book mathematical statistics is scheduled for publication

        0 otherwise

X5 = 1 if book business statistics is scheduled for publication

        0 otherwise

X6 = 1 if book finance is scheduled for publication

        0 otherwise

X7 = 1 if book financial accounting is scheduled for publication

        0 otherwise

X8 = 1 if book managerial accounting is scheduled for publication

        0 otherwise

X9 =1 if book English literature is scheduled for publication

        0 otherwise

X10 = 1 if book German is scheduled for publication

        0 otherwise

Objective:

Max 20 X1+ 30 X2 + 15 X3 + 10 X4 + 25 X5 + 18 X6 + 25 X7 + 50 X8 + 20 X9 + 30 X10

Contraints :

S.t.

30 X1 + 16 X2 + 24 X3 +20 X4 + 10 X5 + 40 X9 ≤ 60
40 X1 + 24 X2 + 24 X7 + 28 X8 + 34 X9 + 50 X10 ≤ 40

30 X3 + 24 X4 + 16 X5 + 14 X6 + 26 X7 + 30 X8 + 30 X9 + 36 X10 ≤ 40

X3 + X4 + X5 ≤ 2

X7 + X8 ≤ 1

X1 +X2 = 1

Xi = 0, 1 for all i from 1 to 10

According to excel optimal solution X2 = X5 = X6 = 1 and the projected sales are 73,000 copies.

Managerial Report:

1. If it would be advantages to do so, Susan can be moved off another projected to allow her to work 12 more days, the optimal solution is x₂ = x₈ = 1. This calls for publishing the finite math and managerial accounting texts for projected sales of 80,000 copies.
2. If it would be advantageous to do so, Monica can also be made available for another 10 days.X2, X5, and X8. Projected sales are 105,000 copies.
3. If one or more of the revisions could be postponed for another year, the solution in (2) above does not include any new books. In the long run this would seem to be like a bad approach for the firm. For instance, a constraint could be added to require publication of at least one new book, in the short run.

Managerial Report:-