Calc and Vectors

A professional basketball team plays in a stadium that holds 23,000 spectators. With ticket prices at $60, the average attendance had been 18,000. When ticket prices were lowered to $55, the average attendance rose to 20,000. Based on this pattern, how should ticket prices be set to maximize ticket revenue?

  1. 👍 0
  2. 👎 0
  3. 👁 749
asked by Court
  1. looks like for each $5 decrease in the price, the attendance rises by 2000

    let the number of $5 decreases be n
    the price of a ticket = 60-5n
    attendance = 18000 + 2000n

    revenue = (60-5n)((18000+2000n)
    factoring ....
    = 5(12-n)(1000)(18 + 2n)
    = 5000(12-n)(18+2n)
    = 5000(216 + 6n - 2n^2)

    d(revenue)/dx = 5000(6 - 4n)
    = 0 for a max of revenue
    4n = 6
    n = 3/2
    I would assume that the price change would stay as whole multiples of 5 , so I would round this up to 2

    but we defined as the number of decreases, so there should be 2 decreases of $5 or a decrease of $10
    The tickets should sell at $50.00

    check:
    at $60, attendance = 18000, revenue = 1,080,000
    at $55, attendance = 20000, revenue = 1,100,000
    at $50 , attendance = 22000, revenue = 1,100,000

    So they actually have the same revenue at $55 as at $50
    Now if we were allowed to use the actual mathematical answer of 3/2 decreases, we would have a decrease of (3/2)(5) or $7.50
    for a ticket cost of 52.50 , and an attendance of
    21000 and a revenue of $1,102,500

    I will leave the interpretation of the question up to you.

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A baseball team plays in a stadium that holds 53,000 spectators. With ticket prices at $10, the average attendance had been 49,000. When ticket prices were lowered to $8, the average attendance rose to 51,000. (a) Find the demand

    asked by Anonymous on July 15, 2012
  2. Calculus

    A baseball team plays in a stadium that holds 51,000 spectators. With ticket prices at $10, the average attendance had been 49,000. When ticket prices were lowered to $8, the average attendance rose to 51,000 a. Find the demand

    asked by Anon on December 5, 2017
  3. Calculus study

    A baseball team plays in a stadium that holds 52000 spectators. With the ticket price at $9 the average attendance has been 21000. When the price dropped to $6, the average attendance rose to 26000. a) Find the demand function

    asked by Juan on March 30, 2015
  4. math (calc)

    A baseball team plays in a stadium that holds 70000 spectators. With the ticket price at $11 the average attendance has been 30000. When the price dropped to $9, the average attendance rose to 35000. a) Find the demand function

    asked by Anonymous on November 29, 2017
  5. math

    A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $12 the average attendence has been 29000. When the price dropped to $9, the average attendence rose to 33000. Assume that attendence is

    asked by Andrea on June 19, 2019
  6. Calculus

    A baseball team plays in a stadium that holds 68000 spectators. With the ticket price at $11 the average attendence has been 27000. When the price dropped to $10, the average attendence rose to 34000. Assume that attendence is

    asked by Mia on October 15, 2016
  7. math .... mad HARD

    a football stadium seats 60,000 fans.about 1/4 of the fans pay $100.00 per ticket,1/2 of the fans pay $70.00 per ticket, and the remainder pay about $40.00 per ticket.about how much money will the team collect on a day when there

    asked by jafranny on February 20, 2010
  8. Calulus

    Hi there I need help on my calculus homework and this week, we were working on partial derivative. I don't know how to approach this word problem and set it into a maximum or minimum. Well I am not too sure if this problem is a

    asked by shylo on October 25, 2009
  9. Math

    A football stadium can seat 80,000 people The stadium sells tickets for luxury suites and general admission. The stadium cannot sell more than 200 lucury suites and no more than 77,000 tickets for regular admission. If a new

    asked by M on January 6, 2015
  10. Maths

    A football match between United and City is watched by 24 000 spectators. Of the 24 000 spectators, 14 112 support United and 8208 support City. The rest of the spectators are neutrals who support neither team. a.Work out the

    asked by Stephen on April 27, 2015

More Similar Questions