4. John sells ice cream bars at the local park. He buys the bars for $1.20 per dozen and sells them for $0.15 each. If it is a rainy day at the park, he can sell nothing; if is overcast, he sells one dezen bars; and if is sunny, he sells two dozen. He can return unsold bars, but on;y gets $0.05 each for them. (He can only buy in dozens).

1. Assume that John is a pessimist, what should he do? Buy:
a) 2
b) 0
c) 1.5
d) 3
e) None of these

2. Assume that John is an optimist (gambler), what should he do? Buy:
a) 0
b) 1
c) 1.5
d) 2
e) 2.5
3. A one-legged, red-nosed tramp approaches John in the park and tells him he can predict the next day’s weather perfectly after he has drunk a shot of “Ripple” wine (cost of one shot: $0.50). If the tramp is telling the truth, should John engage in this transaction?
a) Yes
b) No
c) Not enough information to answer this question.

4. Assume that John is using minimax regret criteria, how many dozen should he buy?

a) 0
b) 1
c) 1.5
d) 2
e) 2.5

5. If the weather bureau’s forecast for the next day is 30 percent chance of rain, 20 percent chance of being sunny, how many dozen bars should he buy for tomorrow?
a) 0
b) 1
c) 2
d) 3

6. The value of perfect information is:
a) 4
b) 20
c) 24
d) 45
e) 54

1. To figure out what John should do if he is a pessimist, we need to consider his potential profits and losses. On a rainy day, he sells nothing and loses the cost of buying bars. On an overcast day, he sells one dozen bars and makes a profit of (12 * $0.15) - (12 * $1.20) = $1.80 - $14.40 = -$12.60. On a sunny day, he sells two dozen bars and makes a profit of (2 * 12 * $0.15) - (2 * 12 * $1.20) = $3.60 - $28.80 = -$25.20. Clearly, John would make a loss no matter what the weather is. Therefore, the best option for John as a pessimist would be to not buy any bars.

Answer: b) 0

2. If John is an optimist (a gambler), he might be willing to take more risks. In this case, he would consider his potential profits and losses. On a rainy day, he sells nothing and loses the cost of buying bars. On an overcast day, he sells one dozen bars and makes a profit of (12 * $0.15) - (12 * $1.20) = $1.80 - $14.40 = -$12.60. On a sunny day, he sells two dozen bars and makes a profit of (2 * 12 * $0.15) - (2 * 12 * $1.20) = $3.60 - $28.80 = -$25.20.

Considering the potential loss on overcast and sunny days, it might be more beneficial for John to not buy any bars on those days. Therefore, the best option for John as an optimist would be to only buy bars on overcast days.

Answer: b) 1

3. To determine if John should engage in the transaction with the tramp to predict the next day's weather, we need to evaluate the value of perfect information. If the tramp's prediction is 100% accurate, John would have perfect information about the weather and could make more informed decisions about buying bars.

However, the cost of the tramp's prediction is $0.50 (the cost of one shot of "Ripple" wine). To determine if it's worth it, we need to compare the potential profits or losses from buying bars based on the tramp's prediction with the cost of the prediction.

If the tramp's prediction leads to profitable decisions (e.g., buying bars on sunny days and not buying bars on rainy days), then it might be worth it. However, if the prediction doesn't significantly improve John's profits, it might not be worth the cost.

Without more information about the accuracy of the tramp's prediction and the potential profits from buying bars based on the prediction, it is not possible to determine if John should engage in this transaction.

Answer: c) Not enough information to answer this question.

4. To determine how many dozen bars John should buy using the minimax regret criteria, we need to consider the potential regrets for each decision (buying a different number of dozen bars) for each possible weather condition.

For each decision, calculate the regret by subtracting the potential profit from the maximum potential profit for each weather condition. Then, choose the decision with the minimum maximum regret.

However, without the potential profits for each decision and weather condition, it is not possible to determine how many dozen bars John should buy using the minimax regret criteria.

Answer: c) Not enough information to answer this question.

5. To determine how many dozen bars John should buy for tomorrow, we need to consider the probability of each weather condition and the potential profits for each decision (buying a different number of dozen bars) for each weather condition.

Since the weather bureau's forecast suggests a 30% chance of rain and a 20% chance of being sunny, we can calculate the expected value for each decision by multiplying the probability of each weather condition by the potential profit for that decision and weather condition. Then, choose the decision with the highest expected value.

Without the potential profits for each decision and the weather conditions, it is not possible to determine how many dozen bars John should buy for tomorrow.

Answer: c) Not enough information to answer this question.

6. The value of perfect information is the difference between the expected value with perfect information and the expected value without perfect information.

Since the potential profits associated with each decision and weather condition are not provided, it is not possible to calculate the value of perfect information.

Answer: c) Not enough information to answer this question.