Your company manufactures bowling balls in Akron, Ohio. The primary raw material is polyurethane that you order from suppliers. The cost to place each order is $250. The price of the material is $4000 per ton delivered to your plant regardless of lot size. Annual demand for polyurethane at your plant is 76,000 tons. Your company uses 4.5% to calculate its annual cost of carrying materials in inventory. What is the optimal lot size in order to minimize the sum of annual ordering costs and inventory carrying costs of polyurethane? What is the total annual cost based on your optimal lot size?

If you supplier offered you a 10% price reduction per order for minimum orders over 500 tons, would you continue to use your optimal lot size or order at least the minimum? Support your decision with calculations.