Jean and Jill's Bakery bake fresh pies every morning. The daily demand for Jean and Jill's apple pies is a random variable with (discrete) distribution, based on past experience, given by:
Demand 5 10 15 20 25 30
Probability 10% 20% 25% 25% 15% 5%
Each apple pie costs Jean and Jill $15 to make and is sold for $20. Unsold apple pies at the end of the day are purchased by a nearby soup kitchen for $12 each. Assume no goodwill cost.
Demand Probability
5 .......... 0.1
10 .......... 0.2
15 .......... 0.25
20 .......... 0.25
25 .......... 0.15
30 .......... 0.05
a) Based on the demand distribution above, how many apple pies should Jean and Jill bake each day to maximize her expected profit?
b) What is the expected profit if Jean and Jill decide to order the profit maximizing (news vendor) quantity?