Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

rashley284

  • one year ago

Problem: 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, 1200 people will attend. If she charges $7, 970 people will attend. How much should she charge per ticket to make the most money?

  • This Question is Closed
  1. LogicalApple
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If you consider these numbers as points, where x = ticket price and y = people then you have P1 = (4, 1200) and P2 = (7, 970) Determine the equation of a line that passes through these points. You will obtain a linear equation of the form y = mx + b. Notice, though, that Profit itself is a function of x and y. In fact Profit = x * y (it equals the number of people multiplied by the ticket price). So your profit equation would be P(x) = x * y = x * (mx + b) Determine the vertex of this profit equation. This will be the point, x (the ticket price) that results in the maximum profit P(x).

  2. rashley284
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What is the exact equation?

  3. LogicalApple
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I meant to say P1 = (5, 1200) ******** Well if the points are (5, 1200) and (7, 970), the slope is (1200 - 970) / (5 - 7) = -115 In point slope form we can write y - y1 = m(x - x1) y - 970 = -115(x - 7) y = -115x + 1775 Our profit is x * y or x * (-115x + 1775) Profit = P(x) = -115x^2 + 1775x This is a parabola with a maximum value of P(x) where x is the x-coordinate of the vertex. Can you determine the vertex of this parabola?

  4. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.