You manage inventory for your company and use a continuous review inventory system to control reordering items for stock. Your company is open for business 300 days per year. One of your most important items experiences demand of 20 units per day, normally distributed with a standard deviation of 3 units per day. You experience a lead time on orders from your supplier of six days with a standard deviation of two days. The unit price, regardless of order size, is $4.75. Your ordering cost is $10. Your inventory carrying cost is 20 percent. You have established a service level policy of 97.5 percent on this item. Use a. What is your optimal order quantity? (Round up your answer to the next whole number.) b. What is your reorder point? (Round your answer to the nearest whole number.) c. How much safety stock do you carry? (Do not round intermediate calculations. Round up your answer to the next whole number.) \begin{tabular}{|ccc|} \hline TABLE 7-2 & Standard Deviations and Probabilities & \\ \hline \begin{tabular}{l} Z= Number of \\ Deviations Required \end{tabular} & \begin{tabular}{c} Probability of Being \\ in Stock \end{tabular} & \begin{tabular}{c} Probability of \\ Stockout \end{tabular} \\ \hline 1 & 84.13% & 15.77% \\ \hline 1.04 & 85 & 15 \\ \hline 1.28 & 90 & 10 \\ \hline 1.65 & 95 & 5 \\ \hline 1.96 & 97.5 & 2.5 \\ \hline 2.0 & 97.72 & 2.28 \\ \hline 2.33 & 99 & 1 \\ \hline 3.0 & 99.86 & 0.14 \\ \hline \end{tabular} b. What is your reorder point? (Round your answer to the nearest whole number.) c. How much safety stock do you carry? (Do not round intermediate calculations. Round up your answer to the next whole number.) d. What is your average inventory? (Round your answer to the nearest whole number.)