A company requires 5,000 units of a product in a single year. It costs them $100 per order for expenses such as transportation and communication. If the product is carried in inventory, the carrying cost equals 1% of the price of the product for every month that a single unit of the product is held in inventory. This cost is realized primarily from the costs associated with rental and utility costs for the warehouse that stores the inventory. The product costs $200 per unit, and the company works for a total of 300 days in the year. The company currently orders 500 units in each order for a total of 10 orders in the year, but they feel that this order level is not the most economical. They feel that the total inventory costs (the sum of the ordering and the inventory-carrying costs) can be reduced further if they change the order quantity. They also use the continuous inventory system for the product; they want to evaluate whether this is the right system for the product.

Question

A company requires 5,000 units of a product in a single year. It costs them $100 per order for expenses such as transportation and communication. If the product is carried in inventory, the carrying cost equals 1% of the price of the product for every month that a single unit of the product is held in inventory. This cost is realized primarily from the costs associated with rental and utility costs for the warehouse that stores the inventory. The product costs $200 per unit, and the company works for a total of 300 days in the year. The company currently orders 500 units in each order for a total of 10 orders in the year, but they feel that this order level is not the most economical. They feel that the total inventory costs (the sum of the ordering and the inventory-carrying costs) can be reduced further if they change the order quantity. They also use the continuous inventory system for the product; they want to evaluate whether this is the right system for the product. 
Analyze whether the company can further reduce the total inventory costs. If so, what would you recommend the new order quantity to be, and what would be the annual savings in the total inventory costs with the new order quantity? Then evaluate whether the continuous inventory system is the correct inventory management system for this product.