The Cubs are trying to determine which of the following free agent pitchers should be signed: Rick Sutcliffe $($RS$),$ Bruce Sutter $($BS$),$ Dennis Eckersley $($DE$),$ Steve Trout $($ST$),$ Tim Stoddard $($TS$).$ The cost of signing each pitcher and the number of victories each pitcher will add to the Cubs are shown in the below table. Subject to the following restrictions, the Cubs want to sign the pitchers who will add the most victories to the team.

$\backslash$table$[[$Pitcher$,\backslash$table$[[$Cost of Signing Pitcher$],[($$$)$ Millions$]],\backslash$table$[[$Victories added$],[$to Cubs$]],$Handed$],[$RS$,6,6,$Righty$],[$BS$,4,5,$Righty$],[$DE$,3,3,$Righty$],[$ST$,2,3,$Lefty$],[$TS$,2,2,$Righty$]]$

a$.$ At most, $$12$ million can be spent.

b$.$ If DE and ST are signed, then BS cannot be signed.

c$.$ At most two right$-$handed pitchers can be signed.