A grapefruit farmer in central Florida is trying to decide whether to take prote
ID: 3368612 • Letter: A
Question
A grapefruit farmer in central Florida is trying to decide whether to take protective action to limit damage to his crop in the event that the overnight temperature falls to a level well below freezing. He is concerned that if the temperature falls sufficiently low and he fails to make an effort to protect his grapefruit? trees, he runs the risk of losing his entire? crop, which is worth approximately? $75,000. Based on the latest forecast issued by the National Weather? Service, the farmer estimates that there is a? 60% chance that he will lose his entire crop if it is left unprotected.? Alternatively, the farmer can insulate his fruit by spraying water on all of the trees in his orchards. This? action, which would likely cost the farmer C? dollars, would prevent total devastation but might not completely protect the grapefruit trees from incurring some damage as a result of the unusually cold overnight temperatures. The file below contains the assessed distribution of possible damages? (in dollars) to the insulated fruit in light of the cold weather forecast. Of? course, this farmer seeks to minimize the expected total cost of coping with the threatening weather.
Grapefruit.xlsx
?a) Find the maximum value of C below which the farmer will choose to insulate his crop in hopes of limiting damage as result of the unusually cold weather. (please show each step; i know the answer is 35,000 but i dont understand how)
Damage to grapefruit crop if insulated Probability $0 0.30 $5,000 0.15 $10,000 0.10 $15,000 0.15 $20,000 0.30 Total worth $75,000 P(lose entire crop if unprotected) 0.6Explanation / Answer
Solution
Expected damage if not insulated = 75000 x 0.6 = 45000 ……………………………(1)
Expected damage if insulated = 10000 as detailed below ……………………………(2)
Damage, x
0
5000
10000
15000
20000
Total
Probability p(x)
0.3
0.15
0.1
0.15
0.3
1.0
x. p(x)
0
750
1000
2250
6000
10000
(1) and (2) => gain due to insulating = reduction in expected damage = 45000- 10000 = 35000.
So, so far as the cost of insulating is less than or equal to $35,0000, the farmer would minimize the damage. Thus, the maximum value of C below which the farmer will choose to insulate his crop in hopes of limiting damage as result of the unusually cold weather is
$35,0000 ANSWER
DONE
Damage, x
0
5000
10000
15000
20000
Total
Probability p(x)
0.3
0.15
0.1
0.15
0.3
1.0
x. p(x)
0
750
1000
2250
6000
10000