To earn at least $3,200 in revenue, the ticket prices should be $10 or $40.
An equation is a mathematical expression that depicts the relationship between two or more variables and numbers.
(400 - 8p)p Revenue = number of tickets sold * price per ticket
400p - 8p2 = 400p
In the absence of revenue:
400p - 64p² = 0
p = $0 or p = $50
For at least $3200 in revenue:
400p - 8p² = 3200
p = $10 or p = $40
The ticket pricing should be $10 or $40 to generate at least $3,200 in revenue.
Complete question:
Based on past musical productions, a theater predicts selling 400−8p number of tickets when each ticket is sold at p dollars. Using the table from the last question answer the following questions:
1. At what ticket prices should the theater sell the tickets if it must earn at least $3,200 in revenue to break even (to not lose money) on the musical production? Explain how you know.