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A furniture store wants to develop a plan for managing the inventory of one if its staple items, an easy chair. The store manager estimates the monthly demand for the chairs as Normally distributed with mean 400 and a standard deviation of 85. Each chair costs $150 and there is a setup cost of $2500 per order. When an order is placed, it takes 5 months to receive. If the store is out-of-stock the chairs are backordered. The store estimates a penalty cost of $75, which includes the cost of loss of goodwill. The store is using an annual interest rate of 30% for holding costs.

A furniture store wants to develop a plan for managing the inventory of one if its staple items, an easy chair. The store manager estimates the monthly demand for the chairs as Normally distributed with mean 400 and a standard deviation of 85. Each chair costs $150 and there is a setup cost of $2500 per order. When an order is placed, it takes 5 months to receive. If the store is out-of-stock the chairs are backordered. The store estimates a penalty cost of $75, which includes the cost of loss of goodwill. The store is using an annual interest rate of 30% for holding costs.
(a) Find the mean and standard deviation of the demand during lead time. (b) Find the optimal (Q, R) policy under this setting.

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