A manufacturing facility buys 7,500 pressure valves per year from a supplier. Fixed cost of ordering is $250. The holding cost rate is 40% per year per unit based on the purchasing price. The supplier sells the unit for $50 for orders more than 500. The unit price is $55 for orders between 100 and 500. When the order size is below 100, the price is $65. Find the optimal order quantity. Show all details with formula. No guessing.