Jane decides to open a cookie stand on campus to earn extra money. She plans to buy the cookies from a wholesaler for $0.60 apiece and sell them for $1.50 apiece. Since Jane places great importance on the freshness of her products, she returns any unsold cookies back to the wholesaler at the end of the day and gets $0.12 apiece.
(a) Assume that the daily demand for cookies is uniformly distributed between 0 and 150 (assume the demand is continuous and fractional quantities are allowed). How many cookies should Jane buy from the wholesaler in order to maximize her expected profit? (Hint: Recall the second online Newsvendor game that we played. It is even easier to work with Uniform distribution than Normal distribution.)
(b) Given your answer in part (a), how many cookies should Jane expect to sell on average every day? What is the expected number of cookies she will return to the wholesaler on average? What is her expected daily profit? What is her expected daily lost sales?
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