$1.$ Calligraphy Limited sells writing quill boxes to specialty bookshops across the country, with an annual demand of $1,000$ boxes. Currently it makes quarterly orders of $250$ boxes each but would like to reduce inventory costs by placing more economically sized orders. It purchase the boxes from its supplier at $$20/$box$.$ The fixed cost to place an order is $$10.$ The inventory carrying costs include $$0\mathrm{.}50$ per box per year plus cost of capital of $9\%$ of the unit price.

a$.$ What is the optimal Economic Order Quantity that should be used? Is Calligraphy Limited placing orders that are too large or too small?