Question 310862: THE STUDENT COUNCIL AT RAHKENROLE HIGH SCHOOL IS PLANNING A CONCERT. THEY'VE HIRED THE KNOX MOUNTAIN BOYS, A POPULAR LOCAL BAND, FOR $340. A POLL AMONG THE STUDENTS HAS SHOWN THAT IF TICKETS COST $5, 140 PEOPLE WILL COME TO THE CONCERT. FOR EVERY DOLLAR THE TICKET PRICE GOES UP, 10 FEWER PEOPLE WILL COME, AND FOR EVERY DOLLAR IT GOES DOWN, 10 MORE PEOPLE WILL COME.
THE OTHER GROUP WANTS TO RAISE MONEY ON THE CONCERT. HOW MUCH SHOULD HEY CHARGE PER TICKET TO MAXIMIZE THE AMOUNT OF MONEY THEY RAISE? HOW MUCH WILL THEY RAISE AT THAT PRICE?
PLEASE HELP ME, I WOULD REALLY APPRECIATE IT IF YOU DID. PLEASE SOLVE THIS ALGEBRAICALLY AND NOT GUESS AND TEST.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! THE STUDENT COUNCIL AT RAHKENROLE HIGH SCHOOL IS PLANNING A CONCERT. THEY'VE HIRED THE KNOX MOUNTAIN BOYS, A POPULAR LOCAL BAND, FOR $340. A POLL AMONG THE STUDENTS HAS SHOWN THAT IF TICKETS COST $5, 140 PEOPLE WILL COME TO THE CONCERT. FOR EVERY DOLLAR THE TICKET PRICE GOES UP, 10 FEWER PEOPLE WILL COME, AND FOR EVERY DOLLAR IT GOES DOWN, 10 MORE PEOPLE WILL COME.
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Revenue = (price)(attendance)
R(x) = (5+x)(140-10x)
R(x) = 700 + 90x - 10x^2
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Maximum revenue occurs when x = -b/2a = -90/(-20) = 4.5
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THE OTHER GROUP WANTS TO RAISE MONEY ON THE CONCERT. HOW MUCH SHOULD THEY CHARGE PER TICKET TO MAXIMIZE THE AMOUNT OF MONEY THEY RAISE?
They should charge (5+4.5) = $9.50 per ticket
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HOW MUCH WILL THEY RAISE AT THAT PRICE?
R(4.5) = (5+4.5)*(140-45)
Revenue = 9.5*95 = $902.50
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Cheers,
Stan H.
PLEASE HELP ME, I WOULD REALLY APPRECIATE IT IF YOU DID.
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