Question 353710: A theatre owner knows that she can sell 450 tickets if she charges $1 per ticket. She also knows that she can sell 400 tickets if she charges $2 per ticket, and, in general, she will sell 50 less tickets for each extra dollar she charges per ticket. How much should she charge per ticket in order to maximize revenue?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A theatre owner knows that she can sell 450 tickets if she charges $1 per ticket. She also knows that she can sell 400 tickets if she charges $2 per ticket, and, in general, she will sell 50 less tickets for each extra dollar she charges per ticket. How much should she charge per ticket in order to maximize revenue?
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If x = $1, y = 450
If x = $2, y = 450-1*50
If x = $3, y = 450-2*50
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If x = $n, y = 450-(n-1)50
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Revenue = (price per ticket)(number of tickets sold)
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R = n(450-(n-1)50)
R = n(450-50n+50)
R = 500n - 50n^2
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Maximum Revenue occurs when n = -b/2a = -500/(2*-50) = $5
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She should charge $5 for each ticket.
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Cheers,
Stan H.
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