The user link cost functions are:

ca$($fa$)=$ fa $+35,$ cb$($fb$)=$ fb $+25,$ cc$($fc$)=2$fc $+30.$

$($a$).$ Compute the user$-$optimizing $($U$-$O$)$ path flow pattern and the link flows corresponding to

this path flow pattern.

$($b$).$ Is the U$-$O pattern you computed in $($a$)$ also a system$-$optimizing $($S$-$O$)$ pattern? Why or why

not? If not, then find the S$-$O path flow pattern and the corresponding link flow pattern.