PLEASE DO B, C, AND D 2. Suppose that during a football game, lemonade sells for

Question

PLEASE DO B, C, AND D

2. Suppose that during a football game, lemonade sells for $20 per gallon but only costs $5 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 1/10, 11 gallons with probability 4/10, 12 gallons with probability 2/10, 13 gallons with probability 2/10, and 14 gallons with probability 1/10. 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 and the demand for a game is smaller than or equal to the amount, what is the cost from the game? What if the demand is greater than the amount? (c) What is the corresponding expected cost? (d) When 12 gallons are prepared, calculate the expected shortage, the expected leftover quantity and the expected sold quantity (e) What is the smallest amount among 10,11,12,13, and 14 that is good enough to cover lemonade demand for 75% of time (or equivalently, cover all demand with 75% probability)? That is, what is q* such that Pr(D 0.75?

Explanation / Answer

a)

Mean demand = 11.8

b)

payoff table

d)

e)

Pr(D<=q) = 0.75 (cumulative probability of demand should be 0.75.

So q* = 12

X P(X) P(X)*X 10 0.1 1 11 0.4 4.4 12 0.2 2.4 13 0.2 2.6 14 0.1 1.4 1 11.8

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