Hull Baking Company uses $250,000$ lb of sugar annually in its cakes and pastries. The company can order the sugar in $100$ lb bags, at the cost of $$19\mathrm{.}50$ per bag, delivered. The cost of preparing and sending an order is $$50.$ The storage and handling costs amount to $$2$ per bag per year, based on average inventory. The cost of capital for Hull is $12\%.$ Calculate the optimal size of an order.