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Exercises 137
Average weekly
operating costs ($) Utility No. of breakdowns Utility
15 000 1.0 0 1.0
20 000 0.8 1 0.9
30 000 0.3 2 0
35 000 0
(a) The production manager’s responses to questions reveal that, for
him, the two attributes are mutually utility independent. Explain
what this means.
(b) The production manager also indicates that for him k1 = 0.7
(where attribute 1 = operating costs) and k2 = 0.5. Discuss how
these values could have been determined.
(c) Which machine has the highest expected utility for the production
manager?
(8) 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: