$[1/8$ Points$]$

HARMATHAP $1210\mathrm{.}3\mathrm{.}043.$MI$.$

advantage of this position in its pricing strategy. The daily demand function is

$p=2-0\mathrm{.}0004x$

and the daily total cost function is

$C(x)=500+0\mathrm{.}2x+0\mathrm{.}0001x^2$

where $x$ is the number of units.

$($a$)$ Determine Coastal's total revenue, $R(x),$ and profit functions, $P(x),$ in dollars.

$R(x)=$

$P(x)=$

$($b$)$ What profit$-$maximizing price per soda should Coastal charge?

$

per soda

How many sodas per day would it expect to sell at this price?

sodas per day

What would be the daily profits?

$ per day sodas per day it would expect to sell sodas per day daily profits

$

per day

Would Coastal be willing to provide sodas for the festival at this regulated price? Why or why not?

Yes, Coastal would still provide sodas, because the profits would be significantly greater.

Yes, Coastal would still provide sodas, because the profits would be almost the same.

No$,$ Coastal would no longer provide sodas, because the profits would be significantly less.

Fantastic!b