The organized crime boss and perfume king Butch (Stinky) Rose has daily overheads [sic] (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 $40 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.
I have no idea where to really start with this problem. I have tried to multiply the $10 and $900 by 100 so I can add in the $40 easily, but this process did not work.
I do know that the y intercept is -30,000 for this problem, but I need help finding the slope please!!
Thank you so much for any help you can provide it is greatly appreciated!
With each gram of perfume being x, we get:
Revenue: R(x) = 900x
Variable Cost:
Fixed cost (c, or constant): 30,000
P(x) = R(x) - C(x) - c
P(x) = 900x - 10.4x - 30,000
Profit function, or
Do you now see what the slope is, after the above profit equation is compared to the slope-intercept form, or y = mx + b?
The y-intercept is - 30,000 because even if he doesn't buy or sell any perfume, his cost is still $30,000 since he has certain overhead costs.
So, before he even buys any perfume, he's already in the RED, so-to-speak, to the tune of $30,000!