$1.$ An optometrist orders eyeglass frames at a cost of $$40$ per frame and sells each frame for $$70.$ Annual holding cost is $25\%$ 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. Annual demand for frames is normally distributed with mean of $1040,$ and standard deviation of $20\mathrm{.}42.$

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