# Academic help online

The managers of the Lightning Cycle Company are hoping to develop a new bicycle braking system. Two alternative systems have been proposed and, although the mechanics of the two systems are similar, one design will use mainly plastic components while the other will use mainly metal ones. Ideally, the design chosen would be the lightest and the most durable but, because some of the technology involved is new, there is some uncertainty about what the characteristics of the resulting product would be.
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 one 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
utility
Utility
(grams)

(years)

130
1
3
1
180
0.9
2
0.6
250
0.6
1
0
290
0
After further questioning the team leader indicated that he would be indifferent between the following alternatives:
A: A product which was certain to weigh 130 grams, but which had a guaranteed lifetime of only one year; or
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.
(a) What do the team leader”s responses indicate about his attitude to risk and the relative weight which he attaches to the two attributes of the proposed design?
(b) Which design should the team leader choose, given the above responses?
(c) What further analysis should be conducted before a firm recommendation can be made to the team leader?