Problem 1 You are ordering a durable good at the start of every period, which arrives immediately. You would like to order enough so that the probability of stocking out during a period is as low as 2%. a) Calculate S*, expressing it in terms of p and o. b) Suppose now the lead time is L = 3 instead of 0. Using the same 2* as part a), calculate the target inventory position. How does the safety stock compare to part a)? c) Under part b), what is the maximum possible space for On-hand Inventory that you may need at your warehouse? Hint: This is the all the inventory that would arrive if the demand suddenly dropped to 0 indefinitely. Problem 2 You designed a new meal replacement drink and turned it into a small business, selling it online in non-perishable plastic bottles. You own the brand but outsource all production to a contract packager (\"copacker\"). Each time you make a purchase order from the copacker, you pay a fixed cost of K = $400 (mostly for the cost of driving a truck) and variable cost of = $2 per bottle produced. You offload each truck shipment into your empty garage and hence face no storage or processing costs. However, you value your capital at the interest rate of 0.5% per month. a) Since you sell your drinks using a subscription service, you know that you will face a steady demand of A = 5000 bottles per month, with no variability in the demand (the existing customers have already committed to their subscriptions, and you are not taking new customers for now). What quantity @ should you order from the copacker each time? Assume that your garage has infinite space and that you can fit up to 60000 bottles into a truck. b) You collect p = $3 for each bottle sold (after accounting for outbound shipping). How much profit can you make each month