1. ## Optimization Problem

I'm having trouble with this problem.

A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $12 the average attendance has been 23000. When the price dropped to$10, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.

What ticket price would maximize revenue?

2. On the basis of allowable data the 'average attendance' as function of the ticket price is represented in figure...

... and its value is with good approximation...

$E= 58\cdot 10^{3} - 3\cdot 10^{3}\cdot c$ (1)

The expected revenue is...

$R = E\cdot c = 58\cdot 10^{3}\cdot c - 3\cdot 10^{3}\cdot c^{2}$ (2)

... and its derivative...

$\frac{dR}{dc} = 58\cdot 10^{3} - 6\cdot 10^{3}\cdot c$ (3)

... and it valishes for $c= \frac{58}{6} \approx 9,67$ $... Kind regards $\chi$ $\sigma$ 3. Thanks, but that doesn't work. I have an online assignment that allows me to try as many times as I want to, and it doesn't allow that answer. And actually it was really close, so thank you for kinda leading me in the right direction. It ended up being$9.83