|
Title: A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $9 the aver Post by: Catracho on Jul 25, 2019 A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $9 the average attendance has been 29000. When the price dropped to $7, the average attendance rose to 32000. Assume that attendance is linearly related to ticket price.
Title: Re: A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $9 the Post by: bio_man on Jul 25, 2019 Let x = the ticket cost reduction in $. The ticket price function will be:
Price = $9 - x The demand function (number of spectators) is: p(x) = 27,000 + 5000x The revenue is: R(x) = (Demand)(Price) R(x) = (29,000 + 5000x)(9 - x) = 261,000 + 45,000x + 29,000x - 5,000x^2 R(x) = \(261,000+74,000x-5,000x^2\) To find the optimal revenue, take the derivative of R(x) wrt x, set it to zero, and solve for x. \(R'(x)=74,000-10,000x\) \(-74,000=-10,000x\) \(x=\frac{-74}{-10}=7.4\) Price = $9 - 7.4. Answer is $7.60. |