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The manager at Good stone Tires, a distributor of tires in Illinois, uses a continuous review policy to manage inventory. The manager currently orders 12,000

The manager at Good stone Tires, a distributor of tires in Illinois, uses a continuous review policy to manage inventory. The manager currently orders 12,000 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 400. The replenishment lead time for tires is two weeks. Each tire costs Good stone $40, and the company sells each tire for $80. Good stone incurs a holding cost of 25 percent. 

  1. How much safety inventory does Good stone currently carry? 

  2. At what cost of understocking is the manager's current inventory policy justified? 

  3. How much safety inventory should Good stone carry if the cost of understocking is $80 per tire in lost current and future margin?

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