Question: operation research and probability models. 5. Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of

operation research and probability models.

5. Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of strawberries. Her regular supplier can provide as many cases as she wants. However, because these strawberries already are very ripe, she will need to sell them tomorrow and then discard any that remain unsold. Jean estimates that she will be able to sell 10, 11, 12, or 13 cases tomorrow. She can purchase the strawberries for 3 per case and sell them for 8 per case. Jean now needs to decide how many cases to purchase. Jean has checked the store's records on daily sales of strawberries. On this basis, she estimates that the prior probabilities are 0.2, 0.4, 0.3, and 0.1 for being able to sell 10, 11, 12, and 13 cases of strawberries tomorrow. (No chance to sell less than ten or more than thirteen cases.) (a) Draw the decision tree and write down all the probabilities for the chance nodes, along with the profits of all final nodes. [6 marks] (b) Analyse the tree in the standard way and find the optimal decision policy using the expected profit criterion. [4 marks] 5. Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of strawberries. Her regular supplier can provide as many cases as she wants. However, because these strawberries already are very ripe, she will need to sell them tomorrow and then discard any that remain unsold. Jean estimates that she will be able to sell 10, 11, 12, or 13 cases tomorrow. She can purchase the strawberries for 3 per case and sell them for 8 per case. Jean now needs to decide how many cases to purchase. Jean has checked the store's records on daily sales of strawberries. On this basis, she estimates that the prior probabilities are 0.2, 0.4, 0.3, and 0.1 for being able to sell 10, 11, 12, and 13 cases of strawberries tomorrow. (No chance to sell less than ten or more than thirteen cases.) (a) Draw the decision tree and write down all the probabilities for the chance nodes, along with the profits of all final nodes. [6 marks] (b) Analyse the tree in the standard way and find the optimal decision policy using the expected profit criterion. [4 marks]

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