Question

The owner of Cardo Reef Tours found when the price for a tour was $9 US dollars per person

the average number of customers was 1000 per month. When he reduced his price to $7 US dollars
per person the average number of customers increased to 1500 per month. Assuming that his
demand curve was linear, what price should he charge to obtain the largest monthly revenue?
b. If f(x) = 2x
3 − 24x, find the minimum and maximum values of f in the interval [−3,5].

Answer 1

The answers for your two question problem are:

a. He should charge $7 dollars

b. Maximum value : f(5) = 130

Minimum value : f(2) = -32

Explanation:

First problem

*When he charges $9 , the numbers of customers are an average of 1000

This means the revenue is

1000*$9 = $9000

*When he charges $7 , the numbers of customers are an average of 1500

This means the revenue is

1500*$7 = $10500

Since

$10500 > $9000

The owner should charge $7, to attract more customers and get higher revenue.

Second problem

f(x) = 2x^3 − 24x

To easily solve this problem, we can graph the equation using a calculator or any plotting tool.

Please, see attached picture

The highest point of the graph, in the interval [-3,5] corresponds to

f(5) = 130

and the lowest point :

f(2) = -32