The instructor's master student Jenny works in the meat industry. Jenny is a production manager for her firm. In the beginning of every week, she needs to decide the quantity of "fresh meat" for the week's production by considering the existing inventory. The unit purchase cost of fresh meat is 50 . Demand for each week is random and is characterized by a normal distribution with mean 500 units and standard deviation 100 units. The leftover fresh meat at the end of the week is converted to "frozen meat" at a unit processing cost of 10 to ensure the freshness of the meat. (This means that the inventory of the meat in the beginning of a week, if any, is that of frozen meat.) Customers generally prefer fresh meat to frozen meat. Thus, there will be a discount if some portion of the demand is met with frozen meat. Let's assume that the selling price for fresh meat is 100 and the selling price for frozen meat is 90 . We further assume that the cost of back order is simply the gross margin of fresh meat and the weekly holding cost rate is 5%. If Jenny wants to maximize the expected profit per week, please solve Jenny's problem in the framework of the order-up-to inventory model