$58.12\mathrm{.}4$ Allen$$s Shoe Stores carries a basic black dress shoe for men that sells at an approximate constant rate of $500$ pairs of shoes every three months. Allen$$s current buying policy is to order $500$ pairs each time an order is placed. It costs $$30$ to place an order, and inventory$-$carrying costs have an annual rate of $20$ percent. With the order quantity of $500,$ Allen$$s obtains the shoes at the lowest possible unit cost of $$28$ per pair. Other quantity discounts offered by the manufacturer are listed below:

Order Quantity Price Per Pair

$099$ $$36$

$100199$ $$32$

$200299$ $$30$

$300$ or more $$28$

What is the minimum$-$cost order quantity for the shoes? What are the annual savings of your inventory policy over the policy currently being used?