(Inventory Management) The daily demand for lemonade has a triangle density as follows:The demand is 0 outside of [40,60]; the density increases linearly (starting from 0) between 40and 50 cups, and then decreases linearly between 50 and 60 (back to 0). The profit for lemonadeis $1 per cup, and the cost to get rid of excess lemonade is 20 cents per cup.

a. What is the optimal amount of lemonade to prepare at the beginning of the day?

b. What is the standard deviation of the demand?