E-buy, a popular consumer electronics store in Lawrence, follows a base stock policy for its best selling vacuum cleaner. The weekly demand for this brand of vacuum cleaners is normally distributed with a mean of 10, and a standard deviation of 4. The manufacturer of this vacuum cleaner takes 4 weeks to replenish an order from E-buy. E-buy estimates that the holding cost for the vacuum cleaner is $15/unit/week, while the backorder cost is $10/unit/week.

1) What should be E-buy's target base-stock level to balance their backorder and inventory holding cost? If your answer is not an integer, provide at least three decimal places, e.g., 7.500.

2)Given the optimal base-stock level you calculated in the previous question, what is E-buy's stockout probability for this brand of vacuum cleaners? If your answer is not an integer, provide at least three decimal places, e.g., 7.500.

3)E-buy has realized that they have underestimated the backorder cost. What base-stock level should they choose to achieve a in-stock probability of 0.75? If your answer is not an integer, provide at least three decimal places, e.g., 7.500.