Powered by Koffee $($PBK$)$ is a new campus coffee store. PBK purchases its coffee from a local supplier, Phish Roasters, for a price of $$25$ per bag. PBK has to pay a cost of $$185$ for every delivery order independent of the order size. The holding cost due to warehousing expenses is $$1$ per bag per month on average. The current market price for the coffee sold by PBK is $$50$ per bag. Moreover, PBK estimates that the cost of good will is $$10$ per bag if PBK does not satisfy the market demand. Assume for simplicity that each order takes exactly $2$ months to arrive. PBK estimates the monthly demand for its coffee has a normal distribution with a mean of $50$ and a standard deviation of $10.$ Assume for simplicity that the demand for each month is independent from each other.