12th Calculus
posted by elley on .
it cost you c dollars each to manufacture and distribute backpacks. if the backpacks sell at x dollars each, the number sold is given by
n=(a/xc)+b(100x)
where a and b are certain positive constanst. what selling price will bring a maximum profit?

Profit as a function of x is
P(x) = n (x  c)
= a  cx + 100 bx  bx^2  cx
Maximum profit occurs when dP/dx = 0
2c + 100 b = 2xb
x = c/b + b/50
Check my work.