Problem 1 (30 points): A small bakery sells pies on campus that are produced in-house in a large oven that holds 100 pies. The pies sell at a fairly steady rate of 86 per month, and they cost $2 each to make. Prior to each baking, the oven must be cleaned out, which requires one hour's time for four workers, each of whom is paid $8 per hour. Inventory costs are based on an annual interest rate of 18%. Also, the pies have a shelf life of two months. i. (10 pts) How many pies should be baked for each production run? What is the total annual cost under this policy? ii. (10 pts) The owner of this bakery is thinking about buying a new oven that requires one-half of the cleaning time of the current oven, and has a capacity twice as large as the current one. What is the optimal number of pies to be baked each time in this new oven? iii. (10 pts) The net cost of the new oven (after trading in the current oven) is $350. How many years would it take for the new oven to pay for itself