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

f(x) = 1/200, 0 < x < 200,

a p. d.f. of the continuous type. If the grocer does not have enoughwatermelons to sell to all consumers, she figures that she loses$5.00 in "good-will" 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"? Hint : if X? n, then her profit is (1.00)X +(-0.50)(n-X); but if X > n, her profit is (1.00)n+(-5.00)(X-n). Find the expected value of profit asa function of n and then select n to maximize this.