4. A wine warehouse expects to sell 30,000 bottles of wine in a year. Each bottle costs $9, and there is a fixed charge of $200 per order. If it costs $3 to store a bottle for a year, a) how many bottles should be ordered at a time and b) how many orders should the warehouse place in a year to minimize inventory costs. (Hint: If x is the lot size, the storage cost is the average inventory (x/2) times the individual cost to store each bottle. Also, the reorder cost is the cost of placing an order (the fixed cost plus the variable cost) times the number of times that orders are placed per year (total yearly expected demand divided by the lot size).
