4 -1 points SPreCalc7 3.1.065 A baseball team plays in a stadium that holds 54,0

Question

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

Explanation / Answer

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

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