Rosalie is organizing a circus performance to raise money fo

Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges 5 dollars, 1220 people will attend. If she charges 7 dollars, 1010 people will attend. How much should she charge per ticket to make the most money? (Round your answer to the nearest cent.)

Solution

let price per ticket =p , number of people attending = n

(p₁,n₁)=(5,1220),(p₂,n₂)=(7,1010)

p-p₁=[(p₂-p₁)/(n₂-n₁)](n-n₁)

p-5=[(7-5)/(1010-1220)](n-1220)

p-5=[-2/210](n-1220)

p-5=(-1/105)(n-1220)

p-5=(-1/105)n+(1220/105)

p=(-1/105)n+(1220/105)+5

p=(-1/105)n+(1745/105)

105p=-n+1745

n=1745-105p

revenue= np

revenue =(1745-105p)p

revenue =(1745p-105p²)

revenue =-(105p²-1745p)

revenue =-105(p²-(1745_/105)p)

revenue =-105(p²-(349_/21)p)

revenue =-105(p²-(349_/21)p+(349_/42)²-(349_/42)²)

revenue =-105(p²-(349_/21)p+(349_/42)²)+(105*(349_/42)²)

revenue =-105(p-(349_/42))²+(12789105_/1764)

vertex is (349_/42 ,12789105_/1764)

she should charge 349_/42 dollars per ticket to make the most money

she should charge 8.31 dollars per ticket to make the most money