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A French fish wholesaler buys fresh scallops every day for 20 Euros per kilo and sells it for 30 Euros to customers, mainly gourmet restaurants and delicatessen stores. At the end of each business day, all remaining scallops are sold at a discount price of 10 Euros to local restaurants. From past experience the wholesale manager knows that daily demand for fresh scallops is approximately normally distributed with a mean of 900 kilos and a standard deviation of 50 kilos.
a) How many kilos of fresh scallops should the wholesaler order per day?
b) How would your answer to a) change if local restaurants were willing to pay 20 Euros for all scallops that the wholesaler could not sell during the day?
c) How would your answers to a) and b) change if the variance of scallop demand doubles as the demand becomes more volatile (the mean does not change)?
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