A citrus grower anticipates a profit of $100,000 this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a 20% chance that the temperature 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 at a cost of $5000. Should the grower spend the $5000 and thereby reduce the profit to $95,000?

Question

Sofia Velasquez

Mathematics

21 April, 08:37

A citrus grower anticipates a profit of $100,000 this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a 20% chance that the temperature 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 at a cost of $5000. Should the grower spend the $5000 and thereby reduce the profit to $95,000?

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Travis · Answer 1

The grower should spend the $5,000, thereby reducing the profit to $95,000.

But, this is based on a 20% probability of freezing temperature during the next week.

Step-by-step explanation:

A) If freezing weather happens with a 20% chance, the profit will be reduced to $60,000.

With this probability, the probable loss will be 20% X $40,000 = $8,000.

B) If the grower can protect the fruit against freezing weather at a cost of $5,000, then she should go ahead. Doing this, the profit will be reduced to $95,000 because of the cost.

However, it is worthy to note that freezing weather happens at 20% chance. This implies that the freezing weather might not happen, 80% chance. But, prudence still demands that necessary precautions are taken, and this includes protecting the crop at a cost of $5,000.