Question

A certain paperback sells for $12. The author is paid royalties of 11% on the first 10,000 copies sold, 12.5% on the next 5000 copies, and 19% on any additional copies. Find a piecewise-defined function R that specifies the total royalties if x copies are sold. (Simplify your answer completely.)

Answer 1

Answer:

• 1.32x  for x ≤10,000
• 1.5x for 10,000 < x ≤ 15,000
• 2.28x - 13,530 for x >15,000

Explanation:

• The flat fee for the first 10,000 copies sold is: 11% * $12 = $1.32

If we sell x of books (x ≤10,000) , we have the royalty : 1.32x

So, on 10,000 copies, the royalty is ...   10,000 · $1.32 = $13,200

• 12.5% on the next 5000 copies, the flat fee is: 12.5%*12 = $1.5

if we sell x of books (10000< x ≤15000) , we have the royalty: 1.5x

So, on the next 5000 copies, the royalty is: 1.5*5000 = $ 7500

• 19% on any additional copies, the flat fee is: 19%*12 = $2.28

If we sell x of books, the number of books more than 15,000 is ...

x -15,000

and the additional royalty : 2.28 (x -15,000)

When this is added to the royalty for the first 15,000 books, the expression (for x > 15000) can be simplified to :

2.28 (x -15,000)  + 13,200 + 7500 = 2.28x - 13,530

So the piecewise-defined function R that specifies the total royalties if x copies are sold R(x)

• 1.32x  for x ≤10,000
• 1.5x for 10,000 < x ≤ 15,000
• 2.28x - 13,530 for x >15,000

Hope it will find you well.