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. How much safety inventory does Goodstone currently carry? 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?