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.
