A theatre owner is trying to decide on a ticket price for his next play. The higher the price, the fewer the number of people who will buy tickets. He creates a quadratic function

Answer 1

to model the relationship between the price of the ticket and the number of tickets sold. The function is given by:

\(f(x) = -0.5x^2 + 50x + 1000\)

Where:
- f(x) represents the number of tickets sold at a ticket price of x dollars
- -0.5x^2 represents the decrease in the number of tickets sold as the ticket price increases
- 50x represents the gradual increase in the number of tickets sold as the ticket price decreases
- 1000 represents the maximum capacity of the theatre

Now, the theatre owner can use this function to determine the optimum ticket price that will maximize his revenue. By finding the vertex of the function, he can identify the ticket price that will generate the highest number of ticket sales.