Question

The director of a play must decide how much to charge per ticket. If tickets cost c dollars each, a total of (755c) people will attend the play. Which ticket price will generate the most income?

Answer 1

The ticket price must be kept at $7.5 to maximise revenue generated from the selling of tickets.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The cost of a ticket is represented by c, while the number of people who will attend the party is given by the formula (75-5c). Therefore, the total revenue that will be generated from the sale of the tickets is,

Revenue, (R) = c × (75 - 5c) = 75c - 5c²

Now, to know the maximum of the income, we must differentiate the function and then put it against 0. Therefore, the differentiation of the function will be,

$\dfrac{dR}{dc} = 75-10c$

Now, if we substitute the value of the differentiated function with 0.

$75-10c=0\\\\-10c =-75\\\\c = 7.5$

Hence, the ticket price must be kept at $7.5 to maximise revenue generated from the selling of tickets.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1