Three students wrote an adventure travel guidebook for Alberta and BC.
Two local publishers are interested in marketing it and both anticipate retailing the book for $20.
Publisher "A" offers a straight royalty of 10% (on the retail price) on all book sales.
Publisher "B" offers an 8% royalty for any books sold up to 5,000 copies
and will then increase the royalty to 15% for any copies sold in excess of 5,000.
a) Describe the type of function that will model the authors' income offered by each publisher.
Publisher A: The authors get for each book sold.
. . . . . . . . . This is a linear function.
Publisher B: The authors get for each book sold up to 5,000 books.
. . . . . . . . . They get for each book in excess of 5,000.
. . . . . . . . . This is a lnear piecewise function.
Let = number of books sold.b) Find the functions and
. . Note that function is a piecewise-defined function.
Publisher A: .
Publisher B: this is quite tricky.
For sales up to 5,000, they get: . per book.
For sales in excess of 5,000, they get: . per book.
If , they still get $1.60 for the first 5000 books: 8,000 dollars,
. . plus $3 each for all books over 5000: dollars.
Hence, for dollars.