On Nov 17, 5:22 pm, "danhey...@yahoo.com" <danhey...@yahoo.com> wrote:
> > Since you discard all end of year inventory, B cannot exceed A_n.
In this problem you don't discard all end of year inventory. The place where you get extra M&Ms when you need them is like a very big reservoir that has some fixed capacity C. In this problem, we are essentially assuming that C is large enough that it can cover the deficit from all the years. We will let c(i) denote the number of M&Ms in the reservoir in the ith year. The goal is to find the maximum value of B such that c(n) = C. You only discard M&Ms when the excess, i.e. A_i - B) + c(i-1) > C (which is the excess that the reservoir cannot contain).