Question

Section 5: Finding Max Profit and Break-Even 5. The Class of 2021 is planning a fundraiser this Spring to raise money for Prom! The Seniors are selling tickets to their BBQ during the month of April. They estimate the income and expenses from this fundraiser with the functions, f(x) = -3x2 + 55x and E(x) = 7x + 144, where x represents the price of a ticket. a. What should the seniors charge for a ticket in order to get maximum profit

Answer 1

given the function of the income is ;

$f(x)=-3x^2+55x$$E(x)=7x+144$

to get maximum profit f(x) = E(x)

$\begin{gathered} -3x^2+55x=7x+144 \\ -3x^2+55x-7x-144=0^{} \\ -3x^2+48x-144=0 \end{gathered}$

Divide all terms by -3:

$x^2-16x+48=0$

Factor the last equation :

$\begin{gathered} (x-4)(x-12)=0 \\ x=4 \\ or \\ x=12 \end{gathered}$

As 12 > 4

The price of the ticket = $12