$($Management science and operations$)$ Keith shoe stores carries a basic black dress and shoe for men that sells at an annual demand of $2000$ pairs. Keith's current buying policy is to order $500$ pairs each time an order is placed. An order costs Keith $$30$ to place. The annual carrying cost for each pair over a year period is $20\%$ of the price of a pair that Keith pays. At the order quantity of $500$ pairs, Keith pays the lowest possible unit price of $$28$ per pair that the supplier could offer. Other quantity discounts offered by the supplier are given in the following table.

$\backslash$table$[[$Order quantity,Unit price$],[$Up to $199,$$$32$

Please answer questions a$-$j