Chapter 1.2, Problem 32E

Break-Even Analysis: Disorganized Crime Butch (Stinky) Rose’s counterfeit Chanel $N=22.5$ racket has run into difficulties: It seems that the authentic Chanel $N_{=}^{\text{o}}22.5$ perfume is selling for less than his counterfeit perfume. However, he has managed to reduce his fixed costs to zero, and his overall costs are now $400 per gram plus $30 per gram transportation costs and commission. (The perfume's smell is easily detected by specially trained Chanel Hounds, and this necessitates elaborate packaging measures.) He therefore decides to sell the perfume for $420 per gram to undercut the competition. Specify Stinky’s profit function, $P\left(x\right)$, where x is the quantity (in grams) of perfume he buys and sells, and use your answer to calculate how much perfume should pass through his hands per day in order that he break even. Interpret your answer