Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose m
2 answers:
Let 
be the number of movies, 
be how much Movie Mania charges and 
be how much Movie Time charges and 
be Anna's plan.
<span>Movie Mania charges a subscription fee of $30 and an additional $5 per movie
</span>
<span>Movie Time charges a subscription fee of $25 and an additional $6 per movie
</span>
<span>How many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?
That's
</span>
Expanding it out,
Is there any room there?
There's no possible plan that will do what Anna wants for 5 or more movies, because in that domain Movie Time costs more than Movie Mania. She can squeeze in there between 1 and 4 movies.
I write the answer as:
<span>Movie Mania charges a subscription fee of $30 and an additional $5 per movie
</span>
<span>Movie Time charges a subscription fee of $25 and an additional $6 per movie
</span>
<span>How many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?
That's
</span>
Expanding it out,
Is there any room there?
There's no possible plan that will do what Anna wants for 5 or more movies, because in that domain Movie Time costs more than Movie Mania. She can squeeze in there between 1 and 4 movies.
I write the answer as:
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has two points of discontinuity at
, where
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so as long as , we can cancel
and be left with
. Then as
, we have
The limit exists, so the discontinuity at -1 is removable (so definitely not C or D).
Meanwhile,
does not exist, so the discontinuity at 1 is non-removable, making A the correct answer.