Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past e

Question

Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges 5 dollars, 1160 people will attend. If she charges 7 dollars, 930 people will attend. How much should she charge per ticket to make the most money

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Sarah 3 weeks 2021-11-20T19:44:41+00:00 1 Answer 0 views 0

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    2021-11-20T19:46:11+00:00

    Answer:

      $7.54

    Step-by-step explanation:

    Using the two-point form of the equation of a line, we can write the equation for the number tickets (t) as a function of price (p).

      t = (t2 -t1)/(p2 -p1)(p -p1) +t1

      t = (930 -1160)/(7 -5)(p -5) +1160

      t = -230/2(p -5) +1160

      t = -115p +1735 = -115(p -15 2/23)

    The revenue from ticket sales will be the product of the price and the number of tickets sold:

      r = pt = p(-115)(p -15 2/23)

    This is the equation of a downward-opening parabola with zeros at p=0 and p=15 2/23. The vertex of the parabola (maximum revenue) will be found at a ticket price halfway between these values. The price for maximum revenue is …

      (0 +15 2/23)/2 = 7 25/46 ≈ 7.54

    Rosalie should charge $7.54 per ticket to obtain the most revenue.

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