Answer:
Practical domain: ![v\in[0,230]\ or\ 0\leqslant v\leqslant 230](https://tex.z-dn.net/?f=v%5Cin%5B0%2C230%5D%5C%20or%5C%200%5Cleqslant%20v%5Cleqslant%20230)
Roger can earn $510 at most.
Step-by-step explanation:
We are given the function

Which gives the earnings of Roger when he sells v videos. Since the play’s audience consists of 230 people and each one buys no more than one video, v can take values from 0 to 230, i.e.
![v\in[0,230]\ or\ 0\leqslant v\leqslant 230](https://tex.z-dn.net/?f=v%5Cin%5B0%2C230%5D%5C%20or%5C%200%5Cleqslant%20v%5Cleqslant%20230)
That is the practical domain of E(v)
If Roger is in bad luck and nobody is willing to purchase a video, v=0
If Roger is in a perfectly lucky night and every person from the audience wants to purchase a video, then v=230. It's the practical upper limit since each person can only purchase 1 video
In the above-mentioned case, where v=230, then

Roger can earn $510 at most.