A hardware store buys hex nuts and bolts from the same supplier. The nuts cost $15$ cents each, and the bolts cost $38$ cents each.

The ordering fee is $$100$ for all orders; This includes the cost of paperwork, tracking and receiving orders.

Storage costs are based on $25\%$ annual interest. The hardware store uses an average of $20,000$ nuts and $14,000$ screws annually.

$2\mathrm{.}1$ Determine the optimal size of the orders of nuts and bolts, and the optimal time between orders.

$2\mathrm{.}2$ If both products are ordered and received simultaneously, the $$100$ ordering fee applies to the combined order. Compare the annual ordering and stocking cost if these orders are ordered separately if: both products are ordered when the nuts are

they order; Both products are ordered when the screws are ordered.