Problem setting:

There is an ice cream store. The manager tells the salesman that

Charge $2 for each ice cream in the morning;

Charge $1.5 for each ice cream in the afternoon before 6pm;

Charge $1 for each ice

cream after 6pm.

The store opens 7am-7pm.

The demand follows a Poisson process of lambda=10/hour

The wholesale price of an icecream is $1, the salvage price is $0.5 (unsold units can be returned to the supplier for $0.5 each)

1. Compute the corresponding expected profits for the order quantity Q = 50:150.

2. How many ice creams the manager should order at the beginning of the day, i.e., find the optimal Q that gives the maximum expected profit.