Sunny Groves is a citrus grower in a southern state that has several citrus orchards. Weather forecasters are predicting a significant drop in temperatures over the next two days. The forecast calls for a 25% chance of near-freezing temperatures and a 10% chance of a deep freeze.
The management of Sunny Groves is concerned that the impending bad weather may damage their crop of citrus fruit. If the weather is fine, the company stands to make $1,000,000 revenue for their harvest. There are three options that the company can take in light of the coming weather:
(1)
Do nothing and hope for the best. If the orchards experience near-freezing temperatures, the company will lose half of its crop (and half of the revenue). A deep freeze would destroy all of the fruit (and lead to no revenue). Obviously, taking no precautions costs nothing.
(2)
Take moderate precautions. This involves having many workers placing heaters and warming tents about the orchards. This would cost $50,000 and reduce the potential losses to $200,000 in a near-freeze and $350,000 in a deep freeze.
(3)
Take extensive precautions. This involves purchasing and assembling temporary enclosures, as well as heaters and tents. This would cost $150,000 and would reduce potential losses to no loss of revenue in a near-freeze and $150,000 in a deep freeze.
Create a three-by-three table calculating the net revenue (revenue minus precaution costs) under all combinations of weather and precautions. Find the expected value of the net revenue under each of the precaution options. Which of the three options would you recommend to the management of Sunny Groves and why?