You are the manager of the Manero Paint store, large paint outlet

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You are the manager of the Manero Paint store, large paint outlet. One big demand item is color NUmber 107 (passion fire) latex paint in one-gallon containers. Manero paint sells 10000 containers of this paint every year. Demand is normally distributed with a standard deviation of 2000 units. Passion fire costs 7.50$ per container. The lead time from order to delivery is 10days with a standard deviation of 3 days. Holding costs are 16% per year and the fixed costs of placing an order are 80$. if Manero Paint stocks out of Passion Fire, It incurs 500$ in stockout costs. The replenishment rate is infinite. Use a36 day year.

a. Calculate the optimum order quantity & the optimum safety Stock.