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138 Decision making under uncertainty
Weight Utility Guaranteed lifetime Utility
(grams) (years)
130 1.0 3 1.0
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?
(9) To celebrate the centenary of the local football club, a pottery manufacturer
has decided to produce a commemorative plate. A choice
has to be made on whether to have a large-scale production run or
a small-scale run. For technical reasons only a large- or small-scale
run is possible and it would not be economical, because of other
commitments, to have more than one production run. The manufacturer
has two objectives: (i) to maximize the profits earned from
the plate and (ii) to minimize the number of customers who will
be disappointed because insufficient plates were produced (a large
number of disappointed customers would not be good for customer
goodwill). For simplicity, the potential demand for the plates has