Consider a yoga studio that sells yoga mats. Each yoga mat costs the studio $10.25 if it purchases less than 50 in a single order. If the studio purchases at least 50 but less than 100, the cost is $10.00 per mat. If the studio purchases at least 100 but less than 400, the cost is $9.75 per mat. Finally, if the studio purchases at least 400 mats, the cost is $9.25 per mat. Demand for each mat is estimated to be 450 annually, evenly spaced throughout the year. The ordering costs is $50 per order. The holding cost rate is estimated to be 40% annually.
a. If the company used a fixed order quantity model, calculate the optimal economic order quantity. Show all work.
b. If management decided to order yoga mats on an annual basis (one order per year), how much more would it cost the company? Show all work.