The demand for tickets to an amusement park is given by p = 70 - 0.2q, where p i

Question

The demand for tickets to an amusement park is given by p = 70 - 0.2q, where p is the price of a ticket in dollars and q is the number of people attending at that price. (a) What price generates an attendance of 3,000 people? What is the total revenue at that price? What is the total revenue if the price is $20? (b) Write the revenue function as a function of attendance, q, at the amusement park. (c) What attendance maximizes revenue? (d) What price should be charged to maximize revenue? (e) What is the maximum revenue? Can we determine the corresponding profit? Please show all steps.

Explanation / Answer

1. p = 70 - 0.2q, What price generates an attendance of 3,000 people? p = 70 - 0.2(3000)=10 2.total revenue= 10(3000)=30000 revenue if price is $20= 3000(20)=60000 3. revenue as a function of attendance= pq=( 70 - 0.2q)q 4. what attendance maximizes revenue= d(pq)/dq= 0

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