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A large toy company Müttel currently allows toy retailers to place orders with delivery in 3 weeks

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A large toy company Müttel currently allows toy retailers to place orders with delivery in 3 weeks. The Gigantic Pocket Monster (Gipokmon) is a new toy that Müttel has introduced. TOYS-are-MINE plans to uses the order-up-to model (with a fill-rate target of 99%) to plan orders and deliveries to their retailers.


Given that this is a new toy, sales estimates are somewhat uncertain. The market research team is fairly confident that weekly demand would be normally distributed with a mean of 100 units. However, since this is a new product, demand uncertainty, as characterized by the standard deviation, is harder to estimate and could be either:
i.              standard deviation of 30; or
ii.             ii. standard deviation of 25 units; or
iii.            iii. standard deviation of 20 units.


In order to budget working capital investment in inventories, you are required to provide an estimate of expected on-hand inventories for each level of uncertainty.