What ticket price will maximize the revenue?

Question

the student council plans to run the school talent show to raise money for charity. Last year, tickets sold for $11 each and 400 people attended. The student council has decided to raise the ticket price for this year's talent show. The student council has determined that for every $1 increase in price, the talent show attendance would decrease by 20 people. What ticket price will maximize the revenue?

Answer 1

Let new price be p.  Attendance A(p) will be 400 - 20(p-11) = 620 - 20p.  p>11

Then revenue R(p) will be = pA(p) = 620p - 20p².

Study this; do you agree?

Then the revenue function is a parabola and at its vertex the maximum occurs.

vertex occurs when p = -b/(2a) = -620 /(-40) = $15.50