1. Questions

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 function (price p as a function of attendance x), assuming it to be linear.
P(x)=_____

How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.)
$_________________

  1. 👍
  2. 👎
  3. 👁
Anonymous

  1. k is for thousands
    (49 k, 10) and (51 k, 8)
    slope = (8-10)/(51 k - 49 k) = -1/1k

    p = -(1/k)x+ b
    10 = -(1/k)49 k + b
    59 = b
    so
    p = -(1/k)x + 59 or p = -x/1000 + 59

    r = x p
    r = -x^2/1000 + 59 x
    x^2 -59000 x = 1000 r
    x^2 - 59000 x + 29,500^2 = 1000 r + 29,500^2
    (x-29,500)^2 = 1000(r + 870,250)
    so max r at x = 29,500 people and revenue of 870,250
    then price = 870,250/29,500 = $29.50
    then p =

    1. 👍
    2. 👎
    Damon

  2. By the way there is no need to use calculus for these since you can complete the square to find the vertex of a parabola with algebra 2.

    1. 👍
    2. 👎
    Damon

  4. Oh okay, thank you!

    1. 👍
    2. 👎
    Anonymous

  5. r = x p
    r = -x^2/1000 + 59 x
    x^2 -59000 x = -1000 r
    x^2 - 59000 x + 29,500^2 = -1000 r + 29,500^2
    (x-29,500)^2 = 1000(r - 870,250)
    so max r at x = 29,500 people and revenue of 870,250
    then price = 870,250/29,500 = $29.50

    1. 👍
    2. 👎
    Damon

  6. i feel like you solved for when the stadium holds 59000 not 53000 like in his question hahaha WHICH IS PERFECT BECAUSE MY PROBLEM IS WITH 59000! yay :)

    1. 👍
    2. 👎
    bob

  8. A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $11 the average attendance has been 22000. When the price dropped to $10, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.

    1. 👍
    2. 👎
    Bobby

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A football team lost 9 yards on each of three consecutive plays. What was the team's total change in position for the three plays?

  2. Math

    A stadium manager has signed five acts this year with a combined revenue projection of $1,000,050. The cost for these is expected to average $85,000 per act. How much profit margin does the stadium expect this last year?

  3. 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

  4. precal

    The amount of fans that have entered the stadium of a UT football game after the doors have opened is shown in the table below. t (minutes) attendance 10 40,000 20 60,000 30 70,000 40 80,000 50 85,000 60 90,000 70 95,000 80

  1. 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

  2. Math Calculus

    A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $11 the average attendance has been 22000. When the price dropped to $10, the average attendance rose to 29000. Assume that attendance is

  3. math please help imedietely

    The stadium capacity allows for players, radio and newspaper reporters, and stadium workers in addition to spectators. How many of these people could be at a game? Victory Stadium: Stadium Capacity - 42,500 General Admission

  4. Economics

    1. Use the table below to predict what would happen if airlines and baseball stadiums priced all seats the same instead of using variable-pricing. What would happen to the number of tickets sold? What would happen to the total

  1. Math

    In a twelve-team bowling league, if every team plays every other team four times during the season. How many games must be scheduled?

  2. physics

    A human wave. During sporting events within large, densely packed stadiums, spectators will send a wave (or pulse) around the stadium (Fig. below). As the wave reaches a group of spectators, they stand with a cheer and then sit.

  3. algebra

    You can buy 1 child's ticket, 1 adult's ticket and 1 senior citizen's ticket for a minor league baseball game for $29. Tickets for adults cost 3 times as much as tickets for children. A family of 3 children, 2 adults, and 2 senior

  4. math

    During a dull football game,1/4 spectators were left after 1 hour.During the next hour 20,000 spectators left. there were 1/12 of the original number of spectators still watching the game. how many spectators were originally

You can view more similar questions or ask a new question.