A concert will be held at the end of April. Past experience indicates when tickets are priced at $70, the average attendance is 1400 people. Each $1 increase in price results in 14 fewer people attending. Let x represent the price of a concert ticket. (A) Determine a formula for the linear function, A(x), representing the quantity of tickets sold at a price x dollars. (B) Determine a simplified formula for the revenue function, (p.A)(x), where p(x)=x is the price function and A(x) is the linear function from part (A). (C) Determine the maximum revenue ALGEBRAICALLY (no graphing). What should the venue charge for a ticket to maximize revenue? Include units with your answer.
A concert will be held at the end of April. Past experience indicates when tickets are priced at $70, the average attendance is 1400 people. Each $1 increase in price results in 14 fewer people attending. Let x represent the price of a concert ticket. (A) Determine a formula for the linear function, A(x), representing the quantity of tickets sold at a price x dollars. (B) Determine a simplified formula for the revenue function, (p.A)(x), where p(x)=x is the price function and A(x) is the linear function from part (A). (C) Determine the maximum revenue ALGEBRAICALLY (no graphing). What should the venue charge for a ticket to maximize revenue? Include units with your answer.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A concert will be held at the end of April. Past experience indicates when tickets are priced at $70, the
average attendance is 1400 people. Each $1 increase in price results in 14 fewer people attending. Let
x represent the price of a concert ticket.
(A) Determine a formula for the linear function, A(x), representing the quantity of tickets sold at a
price x dollars.
(B) Determine a simplified formula for the revenue function, (p A)(x), where p(x)=x is the price
function and A(x) is the linear function from part (A).
(C) Determine the maximum revenue ALGEBRAICALLY (no graphing). What should the venue charge
for a ticket to maximize revenue? Include units with your answer.
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