Question

(***) a concert venue holds a maximum of 1000 people. with ticket prices at $30, the average attendance is 650 people. it is predicted that for each dollar the ticket price is lowered, approximately 25 more people attend. what is the maximum possible revenue from this concert? Answers 1. Latifah The maximum possible revenue from this concert is less than$20,000
The correct answer is an option (a)
In this question, we have been given a maximum of 1000 people- With ticket prices at $30_ the concert venue holds average attendance is 650 people: It is predicted that for each dollar the ticket price is lowered, approximately 25 more people attend. We need to find the maximum possible revenue from this concert. Revenue = (attendance/number of tickets sold)(price per ticket) Let y = attendance/number of tickets sold and x = price per ticket. Let m = -25 and a point in our function be (30, 650). From this information, a function in point-slope form would be: y – 650 = -25(x – 30) y = -25x + 750 + 650 y = -25x + 1400 so, the revenue function would be, R(x) = yx R(x) = -25x² + 1400x The maximum of the revenue function is at the vertex. -b/2a = -1400/(-2 * 25) = 28 so, the maximum revenue from this concert: R(28) = -25(28)² + 1400(28) = 19600 Therefore, the revenue from this concert is Less than$20,000
a) Less than $20,000 b) Between S20,000 and S24,000 c) Between S24,000 and S28,000 d) Between S28,000 and$32,000