Regardless of the type of coat a producer of clothes gets paid 20 Euros per coat from the retailer, his variable costs are 5 Euros. If the manufacturer cannot deliver he has to pay 8 Euros penalty per unfulfilled demand unit to the retailer. The expected sales amount is 100,000 pieces with a standard deviation of 15,000, the demands for the different types of coats are uncorrelated. The capacity costs per piece is 1 Euro, the fix cost of capacity is 5.000 Euros. What is the optimal capacity of a machine producing one type of coat, two types of coats and six types of coats?

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