Tomas, the organizer of a sports event, estimates that if the event is announced x days in advance, the revenue obtained will be R(x) thousand dollars, where

The cost of advertising the event for x days isC(x) thousand dollars, where

a. Find the profit function P(x) = R(x) − C(x), and sketch its graph.

b. How many days in advance should Tomas announce the event to maximize profit? What is the maximum profit?

c. What is the ratio of revenue to cost

at the optimal announcement time found in part (b)? What happens to this ratio as x → 0? Interpret these results.

Transcribed Image Text:

R(x) = 400 + 120x - x²