The organized crime boss and perfume king Butch (Stinky) Rose has daily overheads (bribes to corrupt officials, motel photographers, wages for hit men, explosives, and so on) amounting to $30,000 per day. On the other hand, he has a substantial income from his counterfeit perfume racket: He buys imitation French perfume (Chanel No. 22.5) at $10 per gram, pays an additional $20 per 100 grams for transportation, and sells it via his street thugs for $900 per gram. Specify Stinky's profit function, P(x), where x is the quantity (in grams) of perfume he buys and sells.
Can someone please help me set this equation up? The '$20 per 100 grams' is really throwing me off.
that just means $0.20 per gram
Of course, I was overthinking it. Thanks!
To set up the profit function, let's break down the costs and revenues involved.
1. Cost of buying perfume: Stinky buys imitation French perfume at a cost of $10 per gram.
2. Cost of transportation: Stinky pays an additional $20 per 100 grams for transportation, which means he pays $0.2 per gram for transportation.
3. Total cost per gram: The combined cost of buying perfume and transportation is $10 + $0.2 = $10.2 per gram.
Now, let's consider the revenue:
4. Selling price: Stinky sells the perfume for $900 per gram.
To calculate the profit, we subtract the cost from the revenue:
Profit = Revenue - Cost
Since the cost per gram is $10.2 and the revenue per gram is $900, the profit per gram can be calculated as:
Profit per gram = $900 - $10.2
Finally, we can denote the quantity of perfume bought and sold as x (in grams) and set up the profit function, P(x):
P(x) = Profit per gram * x
Substituting the values:
P(x) = ($900 - $10.2) * x
Therefore, Stinky's profit function is P(x) = $889.8x.