An orange grove anticipates a harvest of $160,000 for the year if the temperatur

Question

An orange grove anticipates a harvest of $160,000 for the year if the temperature reamins mild. However the wather forcast indicates a chance of 25% for cold temperatures in the next week. The cold temperature predicicted will reduce the harvest by 15%. Additionally, the freezing temperatures have a 10% chance of occuring. This will reduce the harvest by 35% to $104,000. The grove could protect the oranges from cold temperatures but not the freezing temperatures at a cost of $5,000 taken from the harvest. Determine wether the grove should invest in the protection from the cold temperatures.

Explanation / Answer

Case 1: Grove doesn't invest in protection

Total loss = P(cold temp)*Loss(cold temp) + P(freezing)*loss(freezing)

              = 0.25*0.15*160000 + 0.10*0.35*160000

              = 11600 dollars

Case 2: Grove decides to invest in protection

Total loss = Cost(Protection) + P(freezing)*loss(freezing)

              = 5000 + 0.10*0.35*160000

              = 10600 dollars

thus, loss in case 2 is lesser, thus the grove should invest in protection against cold temperature.

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