It’s new year’s eve, and you’re re-evaluating your finances for the next year. based on previous spending patterns, you know that you spend $1500 per month on average, with a standard deviation of $500, and each month’s expenditure is independently and identically distributed. as a poor college student, you also don’t have any income. how much should you have in your bank account if you don’t want to go broke this year, with probability at least 95%?

An allergy products superstore buys 6000 of their most popular model of air filters each year. the price of the air filters is $18. the cost of ordering and receiving shipments is $12 per order. accounting estimates annual carrying costs are 20% of the price. the supplier lead time is 2 days. the store operates 240 days per year. each order is received from the supplier in a single delivery. there are no quantity discounts. what is the store’s minimum total annual cost of placing orders & carrying inventory?