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Question 321769: The Valley High School student council is sponsoring a dance. They anticipate that 500 students will attend. The ticket price is $3.00, and they estimate that for every $0.20 increase in ticket price, 25 fewer students will attend. What ticket price will maximize the student council’s profit?
$3.25
$3.40
$3.50
$3.80
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The Valley High School student council is sponsoring a dance. They anticipate that 500 students will attend. The ticket price is $3.00, and they estimate that for every $0.20 increase in ticket price, 25 fewer students will attend. What ticket price will maximize the student council’s profit?
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Profit = price*# of tickets sold
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P(x) = (3+0.2x)(500-25x)
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P(x) = 1500 -75x + 100x - 5x^2
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P(x) = -5x^2 + 25x + 1500
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Max occurs when x = -b/2a = -25/-10 = 2.5
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Price for max profit = 3+0.2(2.5) = $3.50
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Cheers,
Stan H.
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$3.25
$3.40
$3.50
$3.80
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