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In a factory, the number of units manufa...

In a factory, the number of units manufactured in a month follows the linear function N = 231D, where N is the number of units produced in the month and D is the number of days elapsed in the month. Which of the following represents 231 in the above equation?

A

The number of units manufactured only in the first day

B

The number of workers working in the factory

C

The number of units manufactured each day of the month

D

The increase in the number of workers in the factory per day

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the given linear function \( N = 231D \), where \( N \) represents the number of units produced in a month and \( D \) is the number of days elapsed in that month. ### Step-by-Step Solution: 1. **Identify the Variables**: - \( N \): Number of units produced in a month. - \( D \): Number of days elapsed in the month. 2. **Understand the Equation**: - The equation \( N = 231D \) indicates that the total number of units produced in a month is directly proportional to the number of days. The constant of proportionality is 231. 3. **Relate to Work Done**: - The equation can be compared to the general formula for work done, which is \( W = R \times T \), where: - \( W \) is the work done (in this case, the total units produced, \( N \)), - \( R \) is the rate (in this case, the number of units produced per day), - \( T \) is the time (in this case, the number of days, \( D \)). 4. **Identify the Rate**: - In our equation \( N = 231D \): - \( N \) corresponds to \( W \), - \( D \) corresponds to \( T \), - Therefore, \( 231 \) corresponds to \( R \). - This means that 231 represents the number of units produced each day. 5. **Conclusion**: - Thus, \( 231 \) in the equation \( N = 231D \) represents the number of units manufactured each day. ### Final Answer: The value \( 231 \) represents the number of units manufactured each day of the month. ---
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