I'm having trouble figuring out how to set up the equation in the following word problem.
Bea Johnson, the owner of the Bea Nice boutique. estimates that when a particular kind of perfume is prices at p dollars per bottle, she will sell
B(p) = 500/p+3 if p is more than or equal to 5.
bottles per month at a total cost of
C(p) = 0.2p^2 +3p +200 dollars.
a) Express Bea's profit B(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?
Once I get part a), I think I can get part b) by differentiating my answer to part a).
My problem is that I do not understand how to set up the equation for part a.
Any help would be greatly appreciated.
Thanks!
Bea Johnson, the owner of the Bea Nice boutique. estimates that when a particular kind of perfume is prices at p dollars per bottle, she will sell
B(p) = 500/p+3 if p is more than or equal to 5.
bottles per month at a total cost of
C(p) = 0.2p^2 +3p +200 dollars.
a) Express Bea's profit B(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?
Once I get part a), I think I can get part b) by differentiating my answer to part a).
My problem is that I do not understand how to set up the equation for part a.
Any help would be greatly appreciated.
Thanks!
