Rohit bakes fresh cakes every morning. The daily demand for his cakes has a discrete distribution:

Demand 4 15 19 25 31 37

Probability 7% 19% 26% 26% 15% 7%

Each cake costs Rohit $9.15 to make and is sold for $27. Given that everyone knows that fresh cake is so much better, unsold cakes at the end of the day are sold to Rohit's brother for 88 cents each (Rohit is tempted to ask his brother what he does with them all, but he isn't sure he wants to know).

a. If Rohit decided to bake 19 cakes each day, what would be his expected profit? Do not round intermediate calculations. Round your answer to 2 decimal places (so $15.188 is rounded to $15.19).

b. Based on the demand distribution above, how many cakes should Rohit bake each day to maximize his expected profit?