A firm faces an average demand of 12 units per day with a standard deviation of 6 per day for its most popular product PXYZ. To make PXYZ, the firm buys a commodity XYZ for $40 per unit (there is also a fixed cost of $400 whenever an order for XYZ is placed). The firm uses a 20 percent interest rate for holding inventory. The supplier of commodity XYZ has a 16 days leadtime.

Whenever a customer demands a unit of PXYZ, the firm takes a unit of XYZ, and applies the production process P fairly quickly (assume the production process takes almost no time for our purposes) and produces a unit of PXYZ. If the firm does not have any units of XYZ, it has to backorder the customer demand and reimburses its customer $1/day for each day of delay.

1. Compute the optimal inventory policy the firm should use for XYZ

1. Suppose the supplier reduces the replenishment lead time for XYZ from 16 days to 9 days. How much in annual savings in holding costs will the firm obtain due to this improvement?