AV City stocks and sells a particular brand of laptop. It costs the firm $$625$ each time it places an order with the manufacturer for the laptops. The cost of carrying one laptop in inventory for a year is $$130.$ The store manager estimates that total annual demand for the laptops will be $1500$ units, with a constant demand rate throughout the year. Orders are received within minutes after placement from a local warehouse maintained by the manufacturer. The store pol$-$ icy is never to have stockouts of the laptops. The store is open for business every day of the year except Christmas Day. Determine the following:

a$.$ Optimal order quantity per order

b$.$ Minimum total annual inventory costs

c$.$ The number of orders per year

d$.$ The time between orders $($in working days$)$