Question

The owner of a night club has noticed that immediately after the club opens, as more patrons arrive the revenue starts to increase. However, there is a point where, if there are too many patrons, revenue starts to decline. This may be because it becomes too crowded and people talk so much that they do not place orders, or it becomes too crowded for the serving staff to be able to easily take and fill orders, in other words it becomes so crowded that it is hard for people to move. The owner believes that there may be an optimal number of patrons for the night club. Based on an analysis of the data, you determine that revenue, r, as a function of patrons, p, takes on a function like the following:

r(p) = -0.25 p² + 100 p

What framework will help you find the optimal number of patrons, p?

Assume that the equation above correctly predicts the amount of revenue for a given number of patrons in the night club.

What is the optimal number of patrons?

What is the maximum amount of revenue the night club could receive? $ (be sure to enter a comma, if appropriate).

NEED DONE URGENTLY. TIMED ASSIGNMENT

Answer 1

Plot is attached for reference