95 gearboxes of 39 different types Please have a mercy on me if I am asking self-obvious kind of question, but I really want to know and it bothers me for a while now.
The issue is that I face the following situation at my workplace - the company I am working in assembles transmission gearboxes. The total SKU range of finished goods (i.e. transmission gearboxes) is 39. The daily production capacity is 95 pcs.
Now, the question is how many combinations are there to distribute the production capacity of 95 gearboxes per day among 39 different SKU's?
I sincerely apologize for asking this kind of question and probably I look very ... mmm.. dimwit, but I would be more than happy if you could guide me at least on what should be the line of reasoning look like to estimate the total number of combinations.
P.S. If I add yet another parameter (i.e. 22 workdays in a month), will it lead to combinatorial explosion? 
P.S.S. Can this problem be solved in a reasonable amount of time at all? (i.e. P or NP class?) 
P.S.S.S. Excuse me if I look like a spoiled fellow who wants ready answers but do not have the desire to think for himself - I just do not possess the necessary skillset (although I am constantly trying to increase my level of mathematical culture and knowledge).

Distributing $n=95$ items among $k=39$ types is a classic stars and bars problem. the answer is $$\binom{n+k-1}{n} = \binom{133}{95}.$$
If adding another 22 work-days means you now have $39 \times 22$ types, you can apply the same formula as above. If not, please clarify exactly what you mean...
