6.14 A retail grocer has a daily demand X for a certain food sold by the pound, such that X (measured in hundreds of pounds) has probability density function

(He cannot stock over 100 pounds.) The grocer wants to order 100k of food on a certain day. He buys the food at 6¢ per pound and sells it at 10¢

per pound. What value of k will maximize his expected daily profit?