The University of Oregon girls club soccer team is raffling off a bicycle to raise money for new equipment. If they charge 2 dollars per ticket, they will sell 600 tickets. For each 50 cent increase in ticket price, they will sell 30 fewer tickets. What ticket price should they charge to maximize their income?
The team should charge "" dollars to maximize their income.
2 answers
Ticket price should be 6 dollars so that they sell 360 tickets and get income 2160 dollars.
current price of ticket = $2.00
number of sales = 600
let the number of 50 cent increases be n
price per ticket = 2 +.5n
number of sales = 600-30n
income = (2+.5n)(600-30n)
= 1200 - 60n + 300n - 15n^2
= 1200 + 240n - 15n^2
not sure if you know Calculus, so I will not use that method
short cut:
the n of the vertex is -b/(2a) = -240/-30 = 8
So there should be 8 increases of .50 cents, or a $4.00 increase, which makes the price of each ticket
$6.00
number of sales = 600
let the number of 50 cent increases be n
price per ticket = 2 +.5n
number of sales = 600-30n
income = (2+.5n)(600-30n)
= 1200 - 60n + 300n - 15n^2
= 1200 + 240n - 15n^2
not sure if you know Calculus, so I will not use that method
short cut:
the n of the vertex is -b/(2a) = -240/-30 = 8
So there should be 8 increases of .50 cents, or a $4.00 increase, which makes the price of each ticket
$6.00
1 answer