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

Question

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/x-c)+b(100-x)

where a and b are certain positive constanst.  what selling price will bring a maximum profit?

drwls · Accepted Answer

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.