The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer $($R$)$ and sassafras soda $($S$).$ Two resources are constrained: production time $(T),$ of which she has at most $12$ hours per day; and carbonated water $($W$),$ of which she can get at most $1,500$ gallons per day. A case of root beer requires $2$ minutes of time and $5$ gallons of water to produce, while a case of sassafras soda requires $3$ minutes of time and $5$ gallons of water. Profits for the root beer are $$6\mathrm{.}00$ per case, and profits for the sassafras soda are $$4\mathrm{.}00$ per case. For the production combination of $180$ root beer and $0$ sassafras soda, which resource is slack $($not fully used$)?$

production time $($only$)$

carbonated water $($only$)$

both production time and carbonated water

neither production time nor carbonated water

cannot be determined exactly