A company manufactures widgets, and the number of widgets produced per day can be represented by the function \( W(t) = 50t + 100 \), where \( t \) is the number of hours worked. However, the factory operates only for 8 hours a day. What is the domain of the function in this context, and how many widgets are produced in a single day? Let's think step by step and output the final answer within \boxed{}.
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