In Example 1.5.3, the price of a dOpi media player, in dollars per dOpi, is given as a function of the weekly sales x according to the formula p(x)=450−15x for 0≤x≤30.
(a) Find p−1(x) and state its domain.
(b) Find and interpret p−1(105).
(c) In Example 1.5.3, we determined that the profit (in dollars) made from producing and selling x dOpis per week is P(x)=−15x2+350x−2000, for 0≤x≤30. Find (P∘p−1)(x) and determine what price per dOpi would yield the maximum profit. What is the maximum profit? How many dOpis need to be produced and sold to achieve the maximum profit?