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The dance company has a $10 cover charge, an average of 200 people will attend. For each $0.25 increase in admission price, the average number attending decreases by 1. What should the owner charge in order to make the most money? what is the maximum money that can be earned?

  • math -

    If the price is 10.00 + .25x
    attendance = 200 - x
    money = attendance * price = (200-x)(10.00+.25x)
    = -.25x^2 + 40x + 2000

    this is a parabola with vertex at x = 40/.5 = 80

    at x=80, admission is $30, money = 3600

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