S$1)(20$ points$)$ You are working as an OR analyst for an oil company that is searching for new sites to explore petroleum. You have been asked to select at least $3$ out of $7$ possible sites for oil exploration. Designate each site as S$1,$ S$2,$ S$3,$ S$4,$ S$5,$ S$6,$ and S$7.$ The restrictions are:

Restriction $1.$ Evaluating sites S$1$and S$3$will prevent you from exploring site S$7.$

$$ Restriction $2.$ Evaluating sites S$2$ or S$4$ will prevent you from assessing site S$5.$

Restriction $3.$ Of all the sites, at least $3$ should be assessed.

Restriction $4.$ Do not evaluate site S$4$if both sites S$1$and S$2$are explored.

Assuming that Si$$is a binary variable, that if you explore site$-$i$,$ Si$$is $1,$ and $0$ otherwise. Then write necessary constraintsfor each restriction to the problem. NOT a COMPLETE MODEL with objective function.