Question

Roger is paid $50 to sell videos of a play to an audience after the play is performed.

He also receives $2 for each video he sells.

The play's audience consists of 230 people and each audience member buys no more than 1 video

What is the practical domain of the function?

Show how you determined/defined the practical domain.

What is the most that roger can earn?

Answer 1

Practical domain:
`v\in[0,230]\ or\ 0\leqslant v\leqslant 230`

Roger can earn $510 at most when every member of the audience purchases a video

Explanation:

The function

`E(v)=50+2v`

Gives us Roger's earnings when he sells v videos. Knowing the play’s audience consists of 230 people and also each one buys no more than one video, v can take values from 0 to 230 or. equivalently

`v\in[0,230]\ ,\ 0\leqslant v\leqslant 230`

Those limits become the practical domain of E(v) because if we chose v outside of it, the function would lose validity

If nobody is willing to purchase a video, v=0 and Roger's earings would be

`E(0)=50`

If every person from the audience purchases a video, then v=230 because each person can only purchase 1 video

In that case, where v=230, then

`E(230)=50+2(230)=50+460=510`

Roger can earn $510 at most.