Suppose a decision-maker has the following single attribute utility functions: for money: risk neutral for reliability –

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Suppose a decision-maker has the following single attribute
utility functions:
for money: risk neutral for reliability – the time y
between failures: uy in months=1-e-y
also, your DM is indifferent between the following
alternatives
Machine 1: cost of $10,000; average time between failures of 4
months
Machine 2: cost of $5,000; average time between failures of 1
month
a. Calculate a multi-attribute utility function which fits these
preferences. What assumptions did you have to make to develop the
function? Comment on the relative importance to this DM of money
and reliability.
b. Consider a new option (Machine 3) with a cost of $7000 and an
average time between failures of 2 months. Calculate the
multi-attribute utility of Machine 3. Compare it to that of Machine
1 and 2