Tech Computers, Inc. assembles custom home computer systems. The heat sinks needed are bought for $$12$ each and are ordered in quantities of $650$ units. Annual demand is $5200$ heat sinks$,$ the annual inventory holding cost rate is $$3$ per unit, and the cost to place an order is estimated to be $$50.$ Calculate the following:

a$)$ Average inventory level

b$)$ The number of orders placed per year

c$)$ The total annual inventory holding cost

d$)$ The total annual ordering cost

e$)$ The total annual cost