The Warren W$.$ Fisher Computer Corporation purchases $8,000$ transistors each year as components in minicomputers. The unit cost of each transistor is $$10,$ and the cost of carrying one transistor in inventory for a year is $$3.$ Ordering cost is $$30$ per order. What are

$($a$)$ the optimal order quantity,

$($b$)$ the expected number of orders placed each year, and

$($c$)$ the expected time between orders?

Assume that Fisher operates on a $200-$day working year.