Question 1. John runs a fresh fruit stand at the beach. Unfortunately, his cooling capabilities are limited, hence at the end of the week he has to discard any unsold fruits. John's best-selling items are oranges. Every Monday morning, John buys oranges for the week. He pays 2 Euros per kg of oranges and sells them at 8 Euros per kg. Weekly demand for oranges at the beach stand is normally distributed with a mean of 60 kg and a standard deviation of 25 kg. Calculate the optimal quantity of oranges John should buy on Monday morning to serve customers during the week, the expected units short, and the expected weekly prot. Optimal order quantity: Round your answers to two decimal places. Expected units short: Round your answer to two decimal places. Expected weekly prot: Round your answer to two decimal places.
Question 2. Instead of the optimal order quantity, John bought the expected demand per week in the last season. Calculate the expected units short and the expected prot. Expected units short: Provide your answer with three decimal places. Expected prot: Provide your answer with two decimal places
Question 3. John also oers ready-to-eat mangoes to his customers. They are more expensive than oranges, because they are own in from Asia. He buys the mangoes from a fruit wholesaler at 15 Euros per kilogram. He tracked past demand for mangoes and knows that it is normally distributed with mean 10 kg and a standard deviation of 7 kg. Because mangoes are expensive, John was conservative and decided to buy 6 kg of mangoes per week. Calculate the (implied) service level and the corresponding selling price that John should set.
-Selling price: Round your answer to two decimal places.
Question 4. Assume that John currently sells mangoes at a price of 27 Euros per kg. He came up with the idea that excess fruits, the ones that he could not sell at the beach during the week, are suitable for making juices. Anna, a friend of his, runs a juice bar and oers to buy excess mangoes from John at 5 Euros per kilogram. If John buys the optimal order quantity of mangoes, what is the probability of John not having any mangoes to sell to Ana at the end of the week?