The production planner for Fine Coffees, Inc. produces two coffee blends: American $($A$)$ and British $($B$).$ He can only get $300$ pounds of Colombian beans per week and $200$ pounds of Dominican beans per week. Each pound of American blend coffee requires $12$ ounces of Colombian beans and $4$ ounces of Dominican beans, while a pound of British blend coffee uses $8$ ounces of each type of bean. Profits for the American blend are $$2\mathrm{.}00$ per pound, and profits for the British blend are $$1\mathrm{.}00$ per pound. The goal of Fine Coffees, Inc, is to maximize profits.

Based on this information, What is the objective function equation?

$P=4A+8B$

$P=8A+12B$

$P=2A+1B$

$P=1A+2B$