Question

a distributor of apple juice has 5000 bottle in the store that it wishes to distribute in a month. from experience it is known that demand D (in number of bottles) is given by D = -2000p² + 2000p + 1700. the price per bottle that will result zero inventory is

Answer 1

just solve for p in

-2000p² + 2000p + 1700 = 5000

The problem is that D has a maximum of 2200 when p = 0.5

I suspect a typo somewhere. Is D the monthly demand, or the weekly demand?

Answer 2

let D=5000

D=-2000p^2+2000p+17000
5000=-2000p^2+2000p+17000
divided by 1000
5=-2p^2+2p+17
5-17=-2p^2+2p
-12=-2p^2+2p
2p^2-2p-12=0
divided by 2
p^2-p-6=0
p^2-3p+2p-6=0
p(p-3)+2(p-3)=0
(p-3) (p+2)=0
p-3=0 p+2=0
p=3 p=-2