Question
Suppose that the weather forecast in Exercise 9 indicates a $10 \%$ chance that cold weather will reduce the citrus grower's profit from $\$ 100,000$ to $\$ 85,000$ and a $10 \%$ chance that cold weather will reduce the profit to $\$ 75,000$. Should the grower spend $\$ 5000$ to protect the citrus fruit against the possible bad weather?
Step 1
The probability that cold weather will reduce the grower's profit from $\$100,000$ to $\$85,000$ is $10\%$, which we denote as $P_1 = 0.1$. The corresponding profit in this case is $A_1 = \$85,000$. Show more…
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A citrus grower anticipates a profit of 100,000 dollars this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a $25 \%$ chance that the temperatures will drop below freezing during the next week. Such freezing weather will destroy $40 \%$ of the crop and reduce the profit to 60,000 dollars. However, the grower can protect the citrus fruit against the possible freezing (using smudge pots, electric fans, and so on) at a cost of $\$5000.$ Should the grower spend the $\$ 5000$ and thereby reduce the profit to $\$ 95,000 ?$ [Hint: Compute $E(X)$, where $X$ is the profit the grower will get if he does nothing to protect the fruit.]
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A citrus grower anticipates a profit of $100,000 this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a 25% chance that the temperatures will drop below freezing during the next week. Such freezing weather will destroy 40% of the crop and reduce the profit to $60,000. However, the grower can protect the citrus fruit against the possible freezing (using smudge pots, electric fans, and so on) at a cost of $5,000. Should the grower spend the $5,000 and thereby reduce the profit to $95,000? [Hint: Compute E(X), where X is the profit the grower will get if he does nothing to protect the fruit.]
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