You have been hired as a financial manager by Alpha Company which sells 2,700 of car batteries per year, and places orders for 600 of metals. The Company has no safety stocks. Moreover, the financial analyst estimates a 50% probability of no shortages in each cycle, and the likelihood of inventory shortages of 10, 20, and 30 units as 0.25, 0.15, and 0.10 respectively. The carrying cost per unit per year is $2. The stockout cost is $5, What is the optimal level of safety stock should you recommend? You plan to consider safety stock of 0, 10, 20, and 30 units.