$($Quantity Discount Model$)$ Keith Shoe Stores carries a basic black dress shoe that sells at a constant rate of $500$ pairs of shoes every three months. Keith's current buying policy is to order $500$ pairs each time an order is placed. It costs Keith $$30$ to place an order. The annual holding cost rate is $20\%.$ With the order quantity of $500$ pairs, Keith obtains the shoes at the lowest possible cost of $$28\mathrm{.}00$ per pair. Other quantity discounts ordered by the manufacturer are described as follows:

Order Quantity$$ Price per pair

$0-99$ $$36$

$100-199$ $$32$

$200-299$ $$30$

$300$ or more$$ $$28$ what is the savings of Keith's shoes when using the quantity discount model as opposed to their current pricing structure $(500$ pairs$)2.$ What is the average flow time using the basic setup $($assuming $250$ working days in a year$)$