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Choice B is correct. It’s given that the employee takes $1.5$ minutes to prepare a sandwich. Multiplying $1.5$ by the number of sandwiches, $x$, yields $1.5x$, the amount of time the employee spends preparing $x$ sandwiches. It’s also given that the employee takes $1.9$ minutes to prepare a salad. Multiplying $1.9$ by the number of salads, $y$, yields $1.9y$, the amount of time the employee spends preparing $y$ salads. It follows that the total amount of time, in minutes, the employee spends preparing $x$ sandwiches and $y$ salads is $1.5x+1.9y$. It's given that the employee spends a total of $46.1$ minutes preparing $x$ sandwiches and $y$ salads. Thus, the equation $1.5x+1.9y=46.1$ represents this situation.

Choice A is incorrect. This equation represents a situation where it takes the employee $1.9$ minutes, rather than $1.5$ minutes, to prepare a sandwich and $1.5$ minutes, rather than $1.9$ minutes, to prepare a salad.

Choice C is incorrect. This equation represents a situation where it takes the employee $1$ minute, rather than $1.5$ minutes, to prepare a sandwich and $1$ minute, rather than $1.9$ minutes, to prepare a salad.

Choice D is incorrect. This equation represents a situation where it takes the employee $30.7$ minutes, rather than $1.5$ minutes, to prepare a sandwich and $24.3$ minutes, rather than $1.9$ minutes, to prepare a salad.