P = L + L + w + w
72 = 2(L) + 2(L-4)
Distribute
72 = 2(L) + 2(L) - 8
Add like terms
72 = 4(L) - 8
Subtract 8 from both sides
64 = 4(L)
Divide both sides by 4
16 = L
The length is 16. Now substitute that in the equation for finding w.
w = L - 4
w =
Let
. Then
, and differentiating both sides with respect to
gives
Now, when
, you get
You have
, so
and
. So
Answer:
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.

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.
