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$).$ There are at most $12$ hours per day of production time and $1500$ gallons per day of carbonated water available. 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. What is the objective function?a$.$ P $=3$R $+2$SOb. P $=4$R $+6$Sc$.$ P $=5$R $+5$Sd$.$ P $=2$R $+3$Se$.$ P $=6$R $+4$S