4 Gotham City is trying to determine how many ambulances it should have and how to staff them. Each ambulance may be staffed with paramedics or emergency medical technicians. Paramedics are considered to provide better service and are paid higher salaries. Budgetary limitations have forced the city to choose between the following two alternatives:

Alternative 1 Four ambulances, two staffed with emergency medical technicians and two staffed with paramedics Alternative 2 Three ambulances, all staffed with paramedics The city authorities believe that the following two attributes determine the city’s satisfaction with ambulance service:

Attribute 1 Time until an ambulance reaches a patient Attribute 2 Percentage of ambulance calls handled by paramedics.

Assume that Gotham City’s multiattribute utility function u(x1, x2) exhibits mui and that

The time for an ambulance to reach a patient is always between 0 and 30 minutes. The city authorities are indifferent between

The city authorities are also indifferent between

Assume that if an ambulance is available when a call comes in, then the ambulance will arrive in 5 minutes; if an ambulance is not available when a call comes in, it will arrive in 20 minutes. With three ambulances, one will be immediately available 60% of the time, and with four ambulances, one will be immediately available 80% of the time.
a Determine the city authorities’ multiattribute utility function.
b Which alternative should they choose?

Transcribed Image Text:

u(x1) = 1 2 and 900 u2(x2) = 10,000