We have to determine the quantity that minimizes annual inventory cost when: C=280,000/q + 2,000,000 where q denotes the order size (in dozens) and C is the annual inventory cost.
Inventory can be 0. Many systems of operation like the JIT model are adopted by businesses to keep inventory as low as possible if not at 0.
But in your question equating q to 0 will not minimize C. Actually this is a weird expression for C, as cost usually decreases as inventory is decreased, but here C increases as q is decreased.
The quantity of q to reduce C to the minimum value would ideally be infinity.
The order size, q, cannot be zero, because you cannot divide by 0. In fact, the larger the q value, the smaller the fraction 280,000/q will be and the smaller the annual inventory cost will be.
Imagine a q value of 280,000. Then 280,000/280,000 = 1 and 1 + 2,000,000 would just be 2,000,001.
If we must give an answer, to minimize cost, q should be infinity. However we know that that is not possible, but q should be as large as possible in order to minimize cost.
Thank you Ken5000 and Just a Guide, that makes sense!