An analyst is assessing a DM's utility function for combined present value of cost COST, in units of [10⁸ $], ranging from 0 to 5, and for annual total vehicle travel time TVTT^ann,, in units of [10⁶ veh-hrs], ranging from 0 to 20.

1. What are considered the best and worst paired values of (, )? Your answer should contain two elements, one showing best values of (, ) and a second showing worst values of (, ).

For parts b-d, the analyst wishes to use a function:

(, ) = ((5.0 )/5.0 )1 + (1 )((20.0 )/20.0)2

where the values are exponents.

1. What are the utilities of the values you reported in part a? Show your work.

1. The analyst has determined that the DM is indifferent between Alternative A and Alternative B:

Alternative A: Probability 0.9of incurring (, ) = (0.0, 0.0) Probability 0.1of incurring (, ) = (5.0, 20.0)

Alternative B: Probability 1.0of incurring (, ) = (0,20.0)

What is the value of wfor this DM? Show your work.

1. The analyst has determined that the DM is also indifferent between Alternative C and Alternative D:

Alternative C: Probability 0.5of incurring (, ) = (0.0, 20.0) Probability 0.5of incurring (, ) = (5.0, 20.0)

Alternative D: Probability 1.0of incurring (, ) = (1.5, 20.0)

What is the value of ₁for this DM? Show your work.