A bakery bakes fresh bread every day which costs $1.5 (per loaf) and sells them for $2.5 (per loaf). They bake batches of 15. Any unsold bread can be sold for 20 cents to a charity at the end of the day.

1. For each baking and demand option provided in the below table, calculate the profit and loss.

			Demand
10	20	30	40
Probability	0.2	0.35	0.25	0.20
Baking	15 (1 batch)
30 (2 batches)
45 (3 batches)

2. Suggest how many batches they should bake to maximise profit based on the Maximin criterion. Show your workings.

3. Calculate expected values to determine which baking option to adopt to achieve the maximum expected profit. Show your workings.

4. The daily demand for bread is assumed to be approximately normal, with a mean of 25 and a standard deviation of 8. What would you recommend as the minimum and maximum baking quantities for breads? Explain.

5. The baking policy in the past has been to bake 30 loaves. Based on this policy and information provided in the previous question, what is the probability that some of the bread loaves will be sold to the charity at the end of the day?