Suppose you sell three types of donuts: plain, nut covered

Suppose you sell three types of donuts: plain, nut covered and chocolate covered. The daily demand of each type of donuts is normally distributed and independent of each other. The means and standard deviations are given in the following table:

Assume that the production lead time of making donuts is zero, and you replenish your inventory of donuts every morning (i.e. review period is one day). Besides, you want to achieve a service level of 80% for each type of donuts.

1. If you make three types of donuts at the beginning of the day, how much safety stock do you need to carry in total to achieve a service level of 80% for each type of donuts? 

2. Instead of making three types of donuts at the beginning of the day, you can only make plain donuts and dip plain donuts in nuts or chocolate on demand (assume for no extra cost). If you follow this strategy, how much safety stock do you need to carry in total to achieve a service level of 80% for each type of donuts? 

3. If you follow the strategy in part b, compared to part a, the total safety stock would go down by how much percentage?