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 18% on any additional copies. Find a piecewise-defined function R that specifies the total royalties if x copies are sold.

Please help me figure out the rest of this equation. Here is what I have so far.

R(x)=
_____if 0≤x≤ 10000
_____if 10000 < x ≤ 15000
_____if x > 15000

Any help is appreciated! Thanks!

Answer 1

if 0≤x≤ 10000 : R(x) = $12 * 11% *x

at x = 10000, R(x) = $12 * 11% *10000 = 13200

10000 < x ≤ 15000 : R(x) = 13200 + $12*12.5%*(x-10000)

(The profit made on the first 10000 books + the profit made on books sold above 10000)

at x = 15000, R(15000) = 13200 + $12*12.5%*(15000-10000) = 20700

x > 15000

R(x) = 20700 + 12*.18*(x-15000),
(The profit made on the first 15000 books + the profit made on books sold above 15000)