answer all parts. correct answer shown. need work and step by step please.

Bob is the manager of a popular coffee shop in Santa Monica, and he is thinking about improving its inventory management. Currently, the shop faces a constant demand of 200 pounds of coffee beans per week, for 52 weeks per year. As the coffee beans must be carefully stored, the storage cost is estimated to be $0.1 per pound per week. The shop sources the coffee beans from an external supplier for $5 per pound (procurement). For delivery costs, the supplier offers tiered pricing to incentivize bigger purchases. USC Marshall School of Business BUAD 311 Operations Management Fall 2022 In this question, we will help Bob figure out the optimal order quantity step by step. a. First, let's pretend that the supplier always charged $20 per delivery, no matter how many pounds were ordered. In this case, how many pounds should Bob order each time? How much would he pay in total weekly inventory costs (weekly holding cost + weekly delivery cost)? (5 points) 282.84 pounds \$28.28/week b. Second, let's still pretend that the supplier always charged $20 per delivery, no matter how many pounds were ordered. But Bob can order at most 250 pounds per order. In this case, how many pounds should he order each time? How much would he pay in total weekly inventory costs (weekly holding cost + weekly delivery cost)? (4 points) 250 pounds $28.50/ week c. Third, let's pretend that the supplier always charged $10 per delivery, no matter how many pounds were ordered. In this case, how many pounds should Bob order each time? How much would he pay in total weekly inventory costs (weekly holding cost + weekly delivery cost)? (5 points) 200 pounds \$20/week d. Finally, let's still pretend that the supplier always charged $10 per delivery, no matter how many pounds were ordered. But Bob must order at least 251 pounds each time. In this case, how many pounds should he order each time? How much would he pay in total weekly inventory costs (weekly holding cost + weekly delivery cost)? (4 points) 251 pounds \$20.52/week e. How many pounds should Bob order each time to minimize the inventory costs? (2 points) 251 pounds