The residents of Anarres^1 wish to choose a location for the new bridge. A caref
ID: 1199769 • Letter: T
Question
The residents of Anarres^1 wish to choose a location for the new bridge. A careful examination of their values highlights three fundamental objectives relevant to this decision context: (i) enhancing transportation efficiency, (ii) protecting environment, (iii) maximizing safety. The following table exhibits the residents' rating for each attribute and alternative. The residents' utility functions are ur(t) = t^2 for transportation, u_E(e) = for environment, us(s) = s for safety. Additive independence assumption is justified so that the joint utility function is of the form: where Partition the feasible region of (k_T, k_E) into three regions R_1, R_2. R_3 such that the optimal choice in region R_i, is Alternative i.Explanation / Answer
For alternative 1: U(t,e,s) = kTuT (t)+kEuE (e)+(1-kT-kE)uS(s)
= uT (t)+uE (e)+uS(s) = t2+Öe+s
= 0.42+Ö0.49+0.5 = 0.16 + 0.7 + 0.5 = 1.36
For alternative 2: U(t,e,s) = kTuT (t)+kEuE (e)+(1-kT-kE)uS(s)
= uT (t)+uE (e)+uS(s) = t2+Öe+s
= 0.92+Ö0.25+0.2 = 0.81+ 0.5 + 0.2 = 1.51
For alternative 3: U(t,e,s) = kTuT (t)+kEuE (e)+(1-kT-kE)uS(s)
= uT (t)+uE (e)+uS(s) = t2+Öe+s
= 0.52+Ö0.01+0.6 = 0.25+ 0.1+ 0.6 = 0.95
Here Alternative 2 have more utility function and alternative 3 have low utility.