4 1 points SPreCalc7 31065 A baseball team plays in a stadiu

4 -1 points SPreCalc7 3.1.065 A baseball team plays in a stadium that holds 54,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. My Notes Ask Your Te (a) Find a function that models the revenue in terms of ticket price. (Let x represent the price of a ticket and R represent the revenue.) R(x) (b) Find the price that maximizes revenue from ticket sales. (c) What ticket price is so high that no revenue is generated? Need Help?Waich

Solution

4)

let x represents the price of ticket

attendance = 33000+ 3000(10-x)

=>attendance = 63000 -3000x

(a)

revenue ,R(x)=x(63000 -3000x)

=>R(x)=(63000x -3000x²)

(b)

R(x)=-3000( x²-21x)

R(x)=-3000( x²-21x+(21_/2)²-(21_/2)²)

R(x)=-3000( x²-21x+(21_/2)²)+(3000(21_/2)²)

R(x)=-3000( x-10.5)²+330750

vertex is (10.5,330750)

price of 10.5 dollars per ticket maximises the revenue from ticket sales

(c)

R(x)=0

=>-3000( x²-21x)=0

=>x²=21x

=>x=21

no revenue is generated when price is 21 dollars per ticket