Quantitative Method QA2-2

It seems that you are a student majoring Finance, I am not very familiar with estimating these, and here are my try:

yearly total demand = 8000 units
quantity produced per run = 400 units
Here, it appears to me that 20 run is needed each year.
Given the fact that production capacity is 200 units per day,
and there are 250 working days.
20 run per year is possible.

now, i assume that the demand of 8000 units is distributed uniformly over the year,
( is this the usual practice of these questions? or there are specification at your source of question? )
so, the company should be producing 400 units each run,
wait one-twentith year until these are sold out,
and then start the next production run.
( this is my guess again )

As the holding cost is 50 a year,
assume it can be distributed uniformly over the year,
( a wild guess again)
the holding cost between two production runs will be $2.5
so, first of all, what is the holding cost with current policy?
will it be Sum of an Arimetic Progression?
a = 2.5/400 , d = 2.5/400 , n = 399
(first one sold out immediately after production)
$498.75 with 400 units per run?
total annual inventory cost = $9975 ?

here, the production initiation cost of $120 per run is not counted in holding cost, and it will not affect our result, is this how it should be?

2008-06-25 16:21:56 補充：
only if the above guesses are all correct, will the following be meaningful:
let production plan be K units per run,
run per year = 8000/K,
holding cost between two run = 50/(8000/K) = K/160

2008-06-25 16:22:00 補充：
inventory cost per run : a = (K/160)/K = 1/160, d = 1/160, n = K-1
= (K-1)/2 * K/160
total annual inventory cost = (K-1)/2 * K/160 *8000/K = (K-1)*25
the smaller is K, the smaller is this cost.

2008-06-25 16:22:16 補充：
As this seems not very reasonable, let me try to count production

initiation cost into the so-called total annual inventory cost
production initiation cost = (8000/K) *120
total expenditure: (K-1)*25 + 960000/K
diff it gives 25-960000/K^2
at minimum, K = 20*sqrt(96) ~ 196

2008-06-25 16:22:26 補充：
total cost with policy of 196 units per run is
= (K-1)*25 + 960000/K
~ 9773
total cost with policy of 400 units per run is
= (K-1)*25 + 960000/K
~12375
saves $ 2602 per year

2008-06-25 16:23:08 補充：
p.s. if any of my assumption is wrong, please tell here
if you got solution, please also tell here, and let us all learn more from it
thanks!