Chicago’s Treadway Tires Dealer must order tires from its national warehouse. It costs $10,000 to place an order. Annual tire sales are normally distributed with mean 20,000 and standard deviation...

Chicago’s Treadway Tires Dealer must order tires from its national warehouse. It costs $10,000 to place an order. Annual tire sales are normally distributed with mean 20,000 and standard deviation 5000. It costs $10 per year to hold a tire in inventory, and the lead time for delivery of an order is normally distributed with mean 3 weeks and standard deviation 1 week. Assume that all shortages are backlogged.

 a. Find the (R,Q) policy the company should use to meet a service level where 96% of all demand is met with on-hand inventory.

b. Assume that the company could pay C dollars per year to decrease the variability in lead times to essentially 0. That is, the lead time would then be a certain 3 weeks. What is the most it would be willing to pay (and still meet the service level in part a)?