A cell phone service sells 48 subscriptions each month if their monthly fee is $30. Using a survey, they find that, for each decrease of $1, 6 additional subscribers will join.
a) What is the Demand Function (price as a function of quantity)?
b) What is the Revenue Function (revenue as a function of quantity)?
c) Determine the vertex algebraically (showing your work) and interpret it in the context of this problem.
d) Determine the price of subscriptions that corresponds to the maximum revenue.
e) Plot the Demand and Revenue Functions together, as well as the points that show the maximum revenue and the price that corresponds to the maximum revenue.