Problem $3(30$ Points$)$

A highway project under consideration has three major factors for decision making: $1)$ initial

construction cost, $2)$ commuter time savings, and $3)$ residential displacement. Their range

appears to be:

Initial construction cost: $ $0<=$ C $<=$ $$6,000,000$

Commuter time savings: $0$ hrs$/$day $<=$ S $<=800$ hrs$/$day

Residential displacement: $0<=$ D $<=50$ families

You have determined the single attribute utility for each of the three objectives: Cost $($C$),$

Time savings $($S$)$ and Residential displacement $($D$)$ as:

U

$0$

You have also find that kC $=0\mathrm{.}5$

kS $=0\mathrm{.}6$

kD $=0\mathrm{.}7$

Determine which of the following project is preferred using multi$-$attributes utility formula:

$($a$)($C$,$ S$,$ D$)=(4,000,000,500,20)$ or

$($b$)($C$,$ S$,$ D$)=(5,000,000,300,15)$