2. A bakery needs to decide how many loaves of bread to bake each day. Each loaf costs the bakery $2 to make and sells for $5. Unsold loaves at the end of the day can be sold to a third party at a value of $1 per loaf. The daily demand for the bread has the following distribution: Demand (Number of loaves) 5, 10, 15, 20, 30, 40 Probability 0.05, 0.15, 0.25, 0.25, 0.25, 0.05.

a. Suppose that the bakery has made 30 loaves. What is the marginal value from a 31st loaf?

b. What is the optimal number of loaves for the bakery to make in order to maximize its average profit?