A chemical compounds manufacturer buys a certain raw material. The annual demand for this raw material is normally distributed with mean 5000 tons and standard deviation 120 tons. The raw material costs $75 per ton and the annual interest rate is 25%. The shop pays $1500 for each order placed and the order arrives in 6 weeks. If the raw material stock is out the production is disrupted. The penalty cost of disrupting the production is estimated to be $45 per ton of demanded raw material.

(Assume a year has 52 weeks.)

a. Find the optimal order quantity, reorder point, and safety stock for black dresses.

b. What are the Type I and Type II service levels obtained by the policy in Part (a)?

c.  Estimate a unit penalty cost of not satisfying the demand, so that the resulting (Q, R) policy would yield 98% service level (Type I).