a. (4 points) Calculate ROP and Q. Round each to the nearest lb.

b. (6 points) Your supplier calls you to tell you that they have changed their policy, and now you can only order chocolate in batches of size 100 (so 100, 200, 300, 400, etc.). Now what should you choose for ROP and Q? Again, round to the nearest lb.

c. (2 points) For the values you picked in part b), what is the average inventory level? How much of this is safety stock? Round to the nearest lb.

d. (3 points) (For clarity, your orders are STILL batched as they were in part b). Your boss reminds you that your local refrigeration unit can only hold a maximum of 3,000 lbs of chocolate at any given time. If you picked the amounts given in part b, are you at any risk of exceeding the maximum? Justify your response quantitatively.

e. (6 points) (For clarity, your orders are STILL batched as they were in part b). Seeing that you are making orders quite regularly, your supplier offers you a deal: If you pay a one-time cost at the beginning of the year, they will use priority shipping for the remainder of the year. With Priority Shipping, your deliveries will arrive in 3 days, instead of the usual 1.5 weeks. What is the maximum you would pay for this deal? Round your answer to the nearest dollar.

You run a bakery that sells chocolate cakes. Your secret ingredient is that you use authen- tic Swiss chocolate shipped directly from Zurich, Switzerland. Because the demand for cakes is random, the amount of chocolate you need each week is also random. Based on experience, you estimate that you need on average 150 lbs of chocolate a week, with a standard deviation of 30 lbs. You can assume throughout the problem that demand is normally distributed. Shipping chocolate (and keeping it refrigerated in transit) from Switzerland is expen- sive! Your supplier charges you $3,500 per lb of chocolate, and An additional $700 per shipment for delivery regardless of the shipment size. The supplier delivers in exactly 1.5 weeks whenever called. Storing Swiss chocolate (with refrigeration) costs you $1.50 per lb of chocolate per year. Because your bakery is still quite new, you aim for a very high service-level of 99% to keep customers happy. For reference, the z(.99) = 2.33. = You manage your inventory using an (ROP, Q) inventory system. Assume 52 weeks a year and 7 days a week