Solve the following problem:
Suppose that during a football game, lemonade sells for $15 per gallon but only costs $4 per gallon to make. If they run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a negligible value. Assume that you believe the fans would buy 10 gallons with probability 3/10, 11 gallons with probability 2/10, 12 gallons with probability 2/10, 13 gallons with probability 1/10, and 14 gallons with probability 2/10. You need to decide how many gallons of lemonade to have on hand at the beginning of the game.
(a) What is the mean demand?
(b) If 12 gallons are prepared, what is the expected revenue from a game?
(c) What is the corresponding expected cost?
(d) What is the optimal amount of lemonade to be prepared for a game?
(e) If the optimal amount is prepared for a game, what is the expected loss from overstock?
(f) Now suppose that the demand was normally distributed with mean 800 gallons and variance 250 gallons2. How much lemonade should be prepared?