For the new $200$ that will be built in Istanbul, the management is consig bringing elephants and rhinoceroses $($in Turkish: gergedan$),$ so they need to decide how many of of these animals to bring. Each elephant consumes $2$ tons and each rhinoceros consumes $4$ tons of ta every week. The total available food capacity for these animals will be $80$ tons per week. On the other hand, each elephant requires $4$ hour and each rhinoceros requires $3$ hours of special care every week, naild each ephant requires $4$ hour and each week. The $200$ management is able to find at most $20$ elephants available to be brought to Istanbul. The objective of the management is to get the maximum support from the local government such that they can get $800$ TL per elephant and $600$ TL per rhinoceros per day.

i$.$ Formulate the zoo management's problem using linear programming by clearly defining decisions variables, $(2$ pts$)$ objective function, and $(2$ pts$)$

$$ all relevant constrains. $2$ prs$)$

Without solving the problem, please comment on whether a purchase plan of bringing $18$ elephants and $10$ rhinoceroses can be an optimal plan. $(3$ pts$)$