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anonymous

  • 5 years ago

An average of 40000 people visit Riverside Park each day in the summer. The park charges $21.00 for admission. Consultants predict that for each $1.00 increase in the entrance price, the park would lose an average of 2500 customers per day. I need to find a formula for the daily revenue. Someone help please!!

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  1. anonymous
    • 5 years ago
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    people = 40000 - 2500(x) x is the increase in price price = 21 + x Revenue = people * price = (40,000 - 2500x) * (21 + x) = -2500x^2 - 12500x + 840000

  2. anonymous
    • 5 years ago
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    http://bit.ly/eylJbx

  3. anonymous
    • 5 years ago
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    thanks so much!!!

  4. anonymous
    • 5 years ago
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    Welcome :)

  5. anonymous
    • 5 years ago
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    Hey theres a second part which asks : What ticket price maximizes the revenue from ticket sales

  6. anonymous
    • 5 years ago
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    Okay to maximize revenue you need to take the derivative and set it equal to 0. If you look at the graph I posted, when the derivative is 0, that is the maximum amount that can be made. This is assuming though that for every $1 DECREASE in price, the number of people goes up by 2500. The derivative of -2500x^2 - 12500x + 840000 = -5000x - 12500 5000x = -12500 x = -2.5 Since the x is a negative number, that means the price must be decreased by $2.50 to reach the maximum revenue. So 21 - 2.5 = $18.50 2.50 * 2500 = 6250 $18.50 * 46,250 = $855,625

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