Given the following $2$ constraints, which solution is a feasible solution for a minimization problem?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. What is the objective function?

Question $7$ options:

Max Z $=$ $$5$ R $+$ $$5$ S

Max Z $=$ $$2$ R $+$ $$3$ S

Max Z $=$ $$3$ R $+$ $$2$ S

Max Z $=$ $$4$ R $+$ $$6$ S

Max Z $=$ $$6$ R $+$ $$4$ S

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$(1)14$x$1+6$x$2>=42$

$(2)$ x$1+3$x$2>=6$

Question $6$ options:

$($x$1,$ x$2)=(0\mathrm{.}5,5).$

$($x$1,$ x$2)=(0,4).$

$($x$1,$ x$2)=(2,5).$

$($x$1,$ x$2)=(1,2).$

$($x$1,$ x$2)=(2,1).$