A bakery makes and sells fresh pies every day in a multiple of 50 units. The cost of making each pie is $2.50, and the pies are sold for $7.50 each. Unsold pies at the end of the day will be offered for a quick sale for $0.50 each, and they are always sold out. Based on past experience, the bakery estimates the daily demand for its pies as below.

Demand	100	200	300	400	500	600
Probability	10%	15%	25%	30%	15%	5%

Answer the following questions by showing the detailed calculations:

2. Construct a table of expected profits or losses for each possible demand quantity to determine the optimal number of pies that the bakery should make every day. (3 marks)
4. Confirm your answers in sub-question a) by showing the profit or loss of the closest quantity that the bakery can produce above and below the optimal number (1 mark)
6. Confirm your answers in sub-question a) using a full marginal analysis based on the costs of overestimating and underestimating demands (2 marks)