Question $3$: Set$-$covering problems$$Player Cost$($million$)$Victory Left$/$Right$$Hand$$RS $6$$ $6$ Right$$BS $4$$ $5$ Left$$DE $3$$ $3$ Right$$ST $2$$ $3$ Left$$TS $2$$ $2$ Right$$The New York Yankees are trying to determine which of the following free agent pitchers should be$$signed: Rick Sutcliffe $($RS$),$ Bruce Sutter $($BS$),$ Dennis Eckersley $($DE$),$ Steve Trout $($ST$),$ Tim Stoddard$($TS$).$ The cost of signing each player and the number of victories each pitcher will add to New York$$Yankees are shown in the table below. Subject to the following restrictions, the New York Yankees$$wish to sign the pitchers who will add the most victories to the team. Formulate the mathematical$$model that decides who should they sign.$$Restriction $1$: At most $$12$ million can be spent.$$Restriction $2$: If DE and ST are signed, then BS cannot be signed.$$Restriction $3$: At most two right$-$handed pitchers can be signed.$$Restriction $4$: New York Yankees cannot sign both BS and RS$.$Restriction $5$: If TS is signed, then ST should be signed.