Analyzing Widget Production Rates

In a certain factory, machines A and B produce a certain type of widget. Machine A produces widgets at a rate of $x$ widgets per hour, while Machine B produces widgets at a rate of $y$ widgets per hour.

If Machine A operates for $t_A$ hours and Machine B operates for $t_B$ hours, the total number of widgets produced by both machines combined can be expressed as:

$$ ext{Total Widgets} = (x imes t_A) + (y imes t_B)$$

What can be concluded about the total output of the factory?

Statement (1): The total hours operated by both machines combined is 12 hours, with machine A operating for 8 hours.

Statement (2): The total number of widgets produced by Machine A is twice the number of widgets produced by Machine B.