Question $3$

For the Restaurant Selection Problem introduced in HW$1,$ consider the following set of uncertain alter$-$

natives and their possible outcomes for each criterion, provided below. Using the power additive utility

function introduced in class, compare the two alternatives for different risk tolerance values:

$($a$){}_m=$

$($b$){}_m=30$

Use the weight vector $(w_c,w_s,w_f)$ where :

$w_c=0\mathrm{.}50$

$w_s=0\mathrm{.}20$

$w_f=0\mathrm{.}30$

The value functions for each criterion are given as:

Cost:

$v_c(x)=\frac{H-x}{H-L}=\frac{900-x}{900-100}=\frac{900-x}{800}$

Service: Use $=1\mathrm{.}5$ for service's value function.

$v_s(x)=\frac{1-e^{-\frac{x-4}{}}}{1-e^{-\frac{9-4}{}}}$

Food Quality:

$v_f(x)=\{\begin{array}{cc}\frac{x-3}{4},& 3x<mn\; id="EditorElement\_721711">5</mn>\\ \frac{4x-5}{30},& 5x<mn\; id="EditorElement\_721749">8</mn>\\ \frac{x+10}{20},& 8x10\end{array}$

Table $1$: Set of Alternatives and Their Outcomes