$3.$ The Sandakan Timber company processes $10,000$ logs annually, operating $250$ days per year. The company has estimated that the ordering cost is RM$1,600$ per order, the cost of carrying logs in inventory before they are processed is RM$15$ per log on an annual basis and it takes $4$ days to receive the order from the supplier. Determine the following.

a$.$ The economic order quantity

b$.$ The minimum total annual inventory cost.

c$.$ The optimal number of orders per year

d$.$ The average inventory level

e$.$ The optimal time between orders

f$.$ The amount of logs that should be on hand when an order is placed