Sunday

November 23, 2014

November 23, 2014

Posted by **Anonymous** on Sunday, July 15, 2012 at 1:51pm.

(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.)

$_________________

- Calculus -
**Damon**, Sunday, July 15, 2012 at 4:03pmk 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 =

- Calculus -
**Damon**, Sunday, July 15, 2012 at 4:05pmBy 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.

- Calculus -
**Anonymous**, Sunday, July 15, 2012 at 6:40pmOh okay, thank you!

- Calculus - sign error (does not matter) -
**Damon**, Sunday, July 15, 2012 at 6:49pmr = 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

- Calculus -
**bob**, Wednesday, October 17, 2012 at 11:54pmi 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 :)

**Answer this Question**

**Related Questions**

Calc and Vectors - A professional basketball team plays in a stadium that holds ...

Calulus - Hi there I need help on my calculus homework and this week, we were ...

economics - 1. If average movie attendance is 250 million when prices are $7 a ...

math - The Houston Chronicle on January 13, 2007 reported on Texans' ticket ...

Math - The local baseball team is advertising a special deal on ticket prices. ...

Calculus - A movie theater wants to determine the price per ticket that should ...

math .... mad HARD - a football stadium seats 60,000 fans.about 1/4 of the fans ...

math - A certain sweepstakes ticket has four categories of prizes with the ...

eco - 2. It has been estimated that the price elasticity of demand for ...

Statistics - The relationship between the number of games won during one season...