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 $(\frac{x}{2})$ 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$).$