Question

A store uses the expression -2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere

from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue?

Answer 1

Since the term 2p is negative, the greater is gets, the smaller the final result.

So, you want 2p to be as small as possible, so that you take away as little as possible from 50.

In particular, 2p is as small as possible if p is as small as possible, and our lesser option is 9.

So, if p=9, the revenue is

`-2p+50=-2\cdot 9+50=50-18=32`

Answer 2

The maximum revenue is 32.

p=9 gives the store the maximum revenue

Explanation:

Hi, since the term with the variable p is negative (-2p) the maximum revenue is given by the lower price (p).

So, substituting with the lowest price p=9 in the expression:

-2p + 50

-2(9) +50

-18+50

32

The maximum revenue is 32.

p=9 gives the store the maximum revenue

Feel free to ask for more if needed or if you did not understand something.