I recently came across the following problem on a set of past examination papers for a university module I'm currently taking:
'A video manufacturer produces 8500 video recorders on a continuous production line every month. Each video requires a tape head unit and these are produced very quickly in batches. It costs €13,000 to set up the machinery to produce a batch and €0.30 a month to store and insure a tape head once made. How large should the batch size be to minimize total costs and how often will they have to set up a production run?'
I arrived at the following values: $$r = 8500, K = 13000, h = 0.30.$$
While trying to apply the formula to find the optimal batch size for a continuous EOQ model, that is $$q^* = \left(\frac{2KDr}{h(r-D)}\right)^{1/2},$$ I noticed that only the rate of production per month was given, not the Demand of the product. Is there some way to calculate this problem to get around this roadblock or am I approaching the problem incorrectly?
I've tried applying the regular EOQ formula, that is $$q^* = \left(\frac{2KD}{h}\right)^{1/2},$$ where Demand is the 8500 value, but I ended up with a seemingly unusual value (which may be completely correct given my lack of experience in this field) : I received an answer close to 27,142 and using $q/D$ to find the time gap between orders I arrived upon roughly 0.3 orders per month.
I came here to ask two things: Is there a way to solve the former continuous model question? Or is the latter question using the basic EOQ model formula closer to being correct?
Thank you in advance, this has been bothering me for the past two days.
