An optometrist orders eyeglass frames at a cost of $$40$ per frame and sells each frame for $$70.$ Annual holding cost is $20\%$ of the optometrist's cost of purchasing a frame. Each time frames are ordered, a cost of $$200$ is incurred. Because of lost goodwill, a cost of $$50$ is incurred each time a customer wants a frame that is not in stock. Frames are delivered two weeks after an order is placed with standard deviation of lead time being $1$ day. Assuming the $52$ weeks $=1$ year, and $7$ day $=1$ week. Annual demand for frames is $N(1,040,400).$

a Assuming all shortages are backlogged, determine the order quantity and reorder point.

b Assuming all shortages result in lost sales, determine the order quantity and reorder point.