A grocery store has n watermelons to sell and makes $1.00 on each sale. Say the number of consumers of these watermelons is a random variable with a distribution that can be approximated by

A pdf of the continuous type. If the grocer does not have enough watermelons to sell to all consumers, she figures that she loses $5.00 in goodwill from each unhappy customer. But if she has surplus watermelons, she loses 50 cents on each extra watermelon. What should n be to maximize profit?

f(x) = 200, 0