Revenue is the amount of money a business has coming in. It can be calculated by the number of items sold multiplies to the amount paid for each item.

Question

A concert venue has determined that they usually sell 700 tickets for a concert when the price is at $25.00 per ticket. They notice that each time the price drops by $1.00, they usually sell an additional 50 tickets. Given this possible relationship, determine what price they should charge to earn a maximum revenue. To convincingly solve this problem, I want you to solve the problem numerically (make a table), graphically (make a graph), and algebraically (make and interpret an equation). To start you off on the right foot, I suggest you make a table that clearly displays the revenue given different ticket prices. Include a conclusion.

Answer 1

700 sold for $25 per ticket

750 for $24

800 for $23

(23, 800) and (25,700 are two points on a line

the line's equation is

T -700 = (100/-2)(P-25)

T = -50P +50(25)+700

T = -50P +1950

with Price = zero, 1,950 show up for free

Revenue = TP = (-50P+1950)P = -50P^2 +1950P

R' = (TP)' = 1950-100P = 0

P = 1950/100 = $19.50 is the revenue maximizing price