A candy store owner has daily demand Y for a certain brand of candy sold from the bulk bins. Suppose the owner will never stock more than one crateful of this candy (so it never goes stale), and that a crate can fill 50 bins. We measure Y in terms of fractions of a crate. With these units, Y has density function

f(y)={3y if 0y1 and 0 otherwise.

The grocer can buy a bin's worth of candy for 0.3 dollars and sell a bin's worth for 0.9 dollars. What amount of candy, C, in bins, should the store owner purchase to maximize expected daily profit?


*I've tried differentiating a few ways, but nothing seems to be working. Please help!

Is there a typo with your density function?

It should read 3y^2 if y is greater than or equal to 0, less than or equal to 1. It is 0 elsewhere.

Is the question complete? If the grocer makes a net profit on each bin, he should get as many as possible (50).

Jin - thank you. I knew something about this wasn't right, but wasn't sure......there should be a revenue and/or cost function that moderates the number of bins that the grocer can profitably obtain.....

Nope, that's all I was given. My professor made it up himself. He gave me this to go on too though, when I emailed him.

profit(c)= {(retail price)(y)-(wholesale price)(c) for y less than c
(retail price)(c)-(wholesale price)(c) for y greater than or = to c.


Then he also wrote E(profit(c))= [integral from 0 to c](retail price)(y)-(wholesale price)(c)(3y^2) dy + [integral from c to 1](retail price-wholesale price)(c)(3y^2)dy


But I still have no clue what to do with it. So I'm gonna try and plug stuff in, but if you could help me out too, I would greatly appreciate it! Thanks!