Fly$-$at$-$Night Express uses $10,000$ #$3$ envelopes per month. It costs $$50$ to order and receive a shipment of these envelopes. The envelopes cost $$0\mathrm{.}40$ each, and Fly$-$at$-$Night uses an inventory carrying cost rate of $10\%$ per year. Fly$-$at$-$Night opens $307$ days per year.

a$.$ Determine the:

i$.$ Economic order quantity

ii$.$ The average inventory level, and

iii. The time between orders.

b$.$ What should the re$-$order point be if the envelope supplier takes ten days to deliver?

c$.$ If the usage rate given is an average and the standard deviation of daily usage of envelopes is $75,$ what should the reorder point and safety stock be if Fly$-$at$-$Night wants to take no more than a $5\%$ chance of running out of stock?