Based on the statistical analysis & market forecasting, daily sales of the number of loaves of bread at a bakery has the following probability distribution:

Sales 10 11 12 13 14 15
Probability 0.1 0.1 0.2 0.3 0.2 0.1

problem 1:
Each loaf of bread costs 50 cents & sells for $2.00.
Unsold bread at the end of the day is donated to chartiy, what is the quantity of bread that should be produced to maximize the expected profit?

problem 2:
Health regulations require that unsold bread at the end of the day be disposed at a cost of 10 cents each. Determine the quantity of bread that should be produced to maximize the expected profit in this case.

problem 3:
Daily demand for bread in a large bakery is approximately normally distributed with a mean of 120 loaves and a standard deviation of 10 loaves. Each loaf of bread costs 25 cents and sells for 50 cents. Unsold bread at the end of the day must be disposed at a cost of 10 cents each. Determine the quantity of bread that should be produced to maximize the expected profit.