A small bakery serves very popular fresh meat pies every day. The cost of making each pie is $2, and they are sold for $5 each. Unsold pies at the end of the day will be put for quick sale for $1.00 each, and they are always sold out. The record of the past daily sales of the pies are presented as below.

Answer the following question by showing the calculations:

a. Construct a table of profits or losses for each possible quantity of the pies based on the demands as recorded above. How many pies should the bakery make every day to maximise the profit? (3 marks)

b. Confirm your answer in sub-question a) using a full marginal analysis based the costs of overestimating and underestimating demands (2 marks)

200 250 300 350 Demand Probability 100 10% 150 20% 25% 25% 15% 5% 200 250 300 350 Demand Probability 100 10% 150 20% 25% 25% 15% 5%