Lakeside Bakery bakes fresh pies every morning. The daily demand for its 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 the bakery $6.75 to make and is sold for $17.99.

Unsold apple pies at the end of the day are purchased by a nearby soup kitchen for 99 cents each. Assume no goodwill cost.

a. If the company decided to bake 15 apple pies each day, what would be its expected profit?

b. Based on the demand distribution given, how many apple pies should the company bake each day to maximize its expected profit?

1002W