I need help with question 1 part c please!

1. (20 marks) The daily demand D for vegetarian pies at a bakery ranges between 0 and 5 and has the probability distribution given below. (a) (b) d 0 1 2 3 4 5 po(d) 0.2 0.2 0.3 0.1 0.1 0.1 What is the mean and variance of the demand for vegetarian pies each day? [5 marks] All baking is done at the start of the day so there is no chance to make more during the day, however the bakery has to throw away any unsold pies at the end of the day. If the bakery sells vegetarian pies at $4 per pie and they cost $1 each to produce, what is the mean and variance in the prot from vegetarian pies each day, if they make 5 vegetarian pies? [5 marks] The bakery could make less than 5 pies at the start of the day to reduce wastage but that could possibly leave unfullled demand (assume in this question that the only veg- etarian option the bakery makes is these vegetarian pies and so if a customer wants a vegetarian pie and one is not available then they will walk away from the shop and not buy anything). What is the optimal number of pies (between 1 and 5) to make at the start of the day in order to maximize expected prot? [10 marks]