PROFIT Bea Johnson, the owner of the Bea Nice boutique, estimates that when a particular k...

PROFIT Bea Johnson, the owner of the Bea Nice boutique, estimates that when a particular kind of perfume is priced at pdollars per bottle, she will sell

bottles per month at a total cost of

C (p) =0.2p2 +3p +200 dollars.

a. Express Bea’s profit P(p)as a function of the price p per bottle.

b. At what rate is the profit changing with respect to p when the price is $12 per bottle? Is profit increasing or decreasing at that price?