The manager at Goodstone Tires, a distributor of tires in Illinois, uses a continuous review policy to manage inventory.

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The manager at Goodstone Tires, a distributor of tires in
Illinois, uses a continuous review policy to manage inventory. The
manager currently orders 10,000 tires when the inventory of tires
drops to 6,000. Weekly demand for tires is normally distributed,
with a mean of 2,000 and a standard deviation of 500. The
replenishment lead time for tires is two weeks. Each tire costs
Goodstone $40, and the company sells each tire for $80. Goodstone
incurs a holding cost of 25 percent. At what cost of understocking
is the manager’s current inventory policy justified? How much
safety inventory should Goodstone carry if the cost of
understocking is $80 per tire in lost current and future
margin?