A power plant in Haymana uses coal at the rate of 18,000 tons each month. The plant has a special agreement with a logistic company to transport coals at a cost of $450 per shipment independent of the amount. The supplier offers a discount scheme to the power plant as follows: $1 per ton for orders below 20,000 tons, $0.98 per ton for orders between 20,000 and 40,000 tons, and $0.96 per ton for orders more than 40,000 tons. The plant incurs a holding cost rate of 20% monthly. a) What is the optimal lot size for the power plant and the corresponding annual cost? b) What is the cycle inventory? c) What is the average flow time? d) What is the number of orders given per year? e) What is the reorder interval length? f) Compare with the case when the supplier does not offer quantity discount but sells at $0.96 per ton?