A product which was certain to weigh 130 grams, but which had a guaranteed lifetime of only 1 year. B.A gamble which offered a 0.7 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.3 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.Finally, the team leader said that he would be indifferent between alternatives C and D below. C.A product which was certain to weigh 290 grams, but which had a guaranteed lifetime of 3 years. D.A gamble which offered a 0.9 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.1 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.   Question: Which design should the team leader choose, given the above responses?

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A.A product which was certain to weigh 130 grams, but which had a guaranteed lifetime of only 1 year.

B.A gamble which offered a 0.7 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.3 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.Finally, the team leader said that he would be indifferent between alternatives C and D below.

C.A product which was certain to weigh 290 grams, but which had a guaranteed lifetime of 3 years.

D.A gamble which offered a 0.9 probability of a product with a weight of 130 grams and a guaranteed lifetime of 3 years and a 0.1 probability of a product with a weight of 290 grams and a guaranteed lifetime of 1 year.

 

Question: Which design should the team leader choose, given the above responses?

The leader of Lightning's research and development team has estimated that if the plastic design is
developed there is a 60% chance that the resulting system would add 130 grams to a bicycle's weight
and would have a guaranteed lifetime of 1 year. He also reckons that there is a 40% chance that a
product with a 2-year lifetime could be developed, but this would weigh 180 grams.
Alternatively, if the metal design was developed the team leader estimates that there is a 70% chance
that a product with a 2-year guaranteed life and weighing 250 grams could be developed. However, he
estimates that there is a 30% chance that the resulting product would have a guaranteed lifetime of 3
years and would weigh 290 grams.
It was established that, for the team leader, weight and guaranteed lifetime were mutually utility
independent. The following utilities were then elicited from him:
Weight (grams)
130
180
250
290
Utility
1.0
0.9
0.6
0
Guaranteed lifetime
(years)
3
2
1
Utility
1.0
0.6
0
After further questioning the team leader indicated that he would be indifferent between the
falle
Transcribed Image Text:The leader of Lightning's research and development team has estimated that if the plastic design is developed there is a 60% chance that the resulting system would add 130 grams to a bicycle's weight and would have a guaranteed lifetime of 1 year. He also reckons that there is a 40% chance that a product with a 2-year lifetime could be developed, but this would weigh 180 grams. Alternatively, if the metal design was developed the team leader estimates that there is a 70% chance that a product with a 2-year guaranteed life and weighing 250 grams could be developed. However, he estimates that there is a 30% chance that the resulting product would have a guaranteed lifetime of 3 years and would weigh 290 grams. It was established that, for the team leader, weight and guaranteed lifetime were mutually utility independent. The following utilities were then elicited from him: Weight (grams) 130 180 250 290 Utility 1.0 0.9 0.6 0 Guaranteed lifetime (years) 3 2 1 Utility 1.0 0.6 0 After further questioning the team leader indicated that he would be indifferent between the falle
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