Assignment:
A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cent the price is raised, 20 fewer people go to the movies. The equation is R= -40c to the power (exponent) of 2 + 84c describes the relationship between the cost of the tickets, c dollars, and the amount of revenue, R dollars, that the theatre makes. What price should the theatre charge to maximize revenue?
Provide complete and step by step solution for the question and show calculations and use formulas.