A continuing drought has caused concern for a farmer who must decide whether to
ID: 3247329 • Letter: A
Question
A continuing drought has caused concern for a farmer who must decide whether to plant soybeans, corn, or wheat. Table S2.2 shows the farmer's expected profit ($000s) depending on the crop planted and amount of rainfall that occurs.
Table S2.2
Alternative
State of Natural Rainfall
Low (.30)
Mod. (.40)
Heavy (.30)
Soybeans
15
82
30
Corn
-2
80
40
Wheat
10
88
20
In Table S2.2, using the maximin criterion, which alternative would be chosen?
In Table S2.2, using expected value, which alternative would be chosen?
The farmer thinks that perhaps his estimated profit for planting corn and experiencing low rainfall is wrong. What would the profit for corn under low rainfall need to be in order for the farmer to be indifferent between planting corn and soybeans using the expected value criterion?
A salesman offers the farmer a prediction that will tell him exactly what level of rainfall will occur. The planting season occurs in one month and the salesman promises to deliver the prediction just before the first day of planting. The cost of the prediction is $5,775. Remembering that the profits above are in units of one thousand dollars, should the farmer buy the prediction? Why or why not?
Bill owes Bob $36. Just before Bill pays him the money, he gives Bob the opportunity to play a dice game to potentially win more money. The rules of this game are as follows: If Bob rolls doubles (probability 1/6), Bill will pay Bob double ($72). If he misses doubles on the first try, he can try again or settle for half the money ($18). If he makes doubles on the second try Bill will again pay-up double ($72), but if Bob misses doubles on the second try Bill will only pay him one-third ($12). Should Bob decide to play the dice game with Bill, or insist that he pay the $36 now? Use a decision tree to support your answer.
Alternative
State of Natural Rainfall
Low (.30)
Mod. (.40)
Heavy (.30)
Soybeans
15
82
30
Corn
-2
80
40
Wheat
10
88
20
Explanation / Answer
In Table S2.2, using the maximin criterion, which alternative would be chosen?
max(15,2,10) = 15
hence soyabeans
In Table S2.2, using expected value, which alternative would be chosen?
E(soyabean) = 0.3 *15 + 0.4 *82 +0.3*30 = 46.3
E(corn) = 0.3 *(-2) + 0.4*80 + 0.3*40 = 43.4
E(Wheat) = 0.3 *10 +0.4*88 +0.3*20 = 44.2
since 46.3 is highest
hence Soyabeans
c )the profit for corn under low rainfall = x
0.3 *x + 0.4*80 + 0.3*40 = 46.3
or x = 7.6666 = 23/3
d) 0.3 * 15 + 0.4 * 88 + 0.3 *40 = 51.7
51.7*1000 = 51700
since 5775 < 51700
the farmer should buy the prediction.
State of Natural Rainfall Alternative Low (.30) Mod. (.40) Heavy (.30) Min Soybeans 15 82 30 15 Corn -2 80 40 -2 Wheat 10 88 20 10Related Questions
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