Maximizing RevenuesDate: 07/29/2002 at 22:28:05 From: AK Subject: Max/Min Problem The Boston Red Sox general manager has a dilemma. His team is playing well and will likely make the playoffs. He wants to charge more for tickets during the playoffs to increase revenue for next year to spend on free agents. The team did a survey of fans and found out that for every $1.00 increase in ticket price, 200 fewer fans will attend a single game. What should the Sox charge to maximize revenue if their average ticket price is $18.00 and the average attendance is 21,000 per game? What will the maximum revenue be? Date: 07/30/2002 at 00:12:39 From: Doctor Ian Subject: Re: Max/Min Problem Hi AK, If he doesn't do anything, he'll end up with 21,000 * 18 = 378,000 dollars, right? Suppose he adds $1 to the ticket price. He'll end up with (21,000 - 200) * (18 + 1) = 395,200 dollars. The simplest way to proceed would be to keep adding $1 and dropping 200 tickets sold until the result starts to go down instead of up. Or, you could generalize the situation as a function of the number of dollars added to the ticket price, f(x) = (21,000 - 200*x) * (18 + x) take the derivative with respect to x, and see where the derivative is equal to zero, which will tell you where the function reaches its maximum value. Does that make sense? Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 07/30/2002 at 08:46:33 From: AK Subject: Thank you (Max/Min Problem) Hi, Thank you Dr. Ian. That was very clearly explained! Thanks again. |
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