Question
Sara’s new employer offers two compensation plans. If Sara reports to work in person, her weekly pay per number of hours worked can be modeled by the function c(h)=50+18h
, where c(h)
is the amount of compensation in dollars, and h is the number of hours worked each week. If she chooses to work remotely, the table shows her pay per number of hours worked. Compare the two function models. If Sara wants to maximize her pay, which choice should she make and why, assuming she works exactly 40 hours per week?(1 point)
Responses
Sara should choose to work remotely since can earn an extra $60.00 per week under that pay model.
Sara should choose to work remotely since can earn an extra $60.00 per week under that pay model.
Sara should choose to work in person since she can earn $720.00 per week.
Sara should choose to work in person since she can earn $720.00 per week.
Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.
Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.
Sara should choose to work in person since she can earn $770.00 per week.
, where c(h)
is the amount of compensation in dollars, and h is the number of hours worked each week. If she chooses to work remotely, the table shows her pay per number of hours worked. Compare the two function models. If Sara wants to maximize her pay, which choice should she make and why, assuming she works exactly 40 hours per week?(1 point)
Responses
Sara should choose to work remotely since can earn an extra $60.00 per week under that pay model.
Sara should choose to work remotely since can earn an extra $60.00 per week under that pay model.
Sara should choose to work in person since she can earn $720.00 per week.
Sara should choose to work in person since she can earn $720.00 per week.
Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.
Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.
Sara should choose to work in person since she can earn $770.00 per week.
Answers
GPT-4o mini
To determine which pay plan maximizes Sara's earnings, we need to calculate her compensation for both working in person and working remotely based on the information provided.
1. **In-Person Compensation:**
The function for in-person compensation is given by:
\[
c(h) = 50 + 18h
\]
If Sara works 40 hours per week, we can substitute \( h = 40 \) into the function:
\[
c(40) = 50 + 18(40) = 50 + 720 = 770
\]
So, if Sara works in person for 40 hours, she earns **$770.00**.
2. **Remote Compensation:**
We would need the table of remote compensation rates to calculate Sara's earnings if she works remotely. Since the table is not provided, let's analyze based on the multiple-choice responses given.
We know the following potential outcomes:
- Sara can earn **$720.00** per week when working in person.
- One of the options mentions that she can earn an extra **$60.00** with remote work, which suggests that the remote compensation could be **$720.00**.
- Another option states she can earn an extra **$10.00** per week with remote work, indicating she would earn **$730.00** if that was the remote pay.
- The option also states she can earn **$770.00** when working in person.
From the information provided, based on the calculations:
- If she works in person, she earns **$770.00** per week.
- If she works remotely, depending on the table (which I don't have access to here), but two potential earnings were calculated based on the responses.
However, we do know that the highest amount mentioned for in-person work ($770) is greater than any mentioned amount for remote work ($720 or $730 from suggestions).
Therefore, based solely on the calculations:
**Sara should choose to work in person since she can earn $770.00 per week.**
1. **In-Person Compensation:**
The function for in-person compensation is given by:
\[
c(h) = 50 + 18h
\]
If Sara works 40 hours per week, we can substitute \( h = 40 \) into the function:
\[
c(40) = 50 + 18(40) = 50 + 720 = 770
\]
So, if Sara works in person for 40 hours, she earns **$770.00**.
2. **Remote Compensation:**
We would need the table of remote compensation rates to calculate Sara's earnings if she works remotely. Since the table is not provided, let's analyze based on the multiple-choice responses given.
We know the following potential outcomes:
- Sara can earn **$720.00** per week when working in person.
- One of the options mentions that she can earn an extra **$60.00** with remote work, which suggests that the remote compensation could be **$720.00**.
- Another option states she can earn an extra **$10.00** per week with remote work, indicating she would earn **$730.00** if that was the remote pay.
- The option also states she can earn **$770.00** when working in person.
From the information provided, based on the calculations:
- If she works in person, she earns **$770.00** per week.
- If she works remotely, depending on the table (which I don't have access to here), but two potential earnings were calculated based on the responses.
However, we do know that the highest amount mentioned for in-person work ($770) is greater than any mentioned amount for remote work ($720 or $730 from suggestions).
Therefore, based solely on the calculations:
**Sara should choose to work in person since she can earn $770.00 per week.**