Exercise I: Derivatives in practice
Assume that a stuffed animal manufacturer produces P(x) hundred of stuffed animals when it employs x workers, where P (x) is given by
P (x) = −60 + 5x + 100 , x
for x >= 10.
1. Compute P (10). Why do we assume x >= 10?
2. How many stuffed animals does the company produce when it employs 20 workers?
3. Compute P′(20). Give its unit and interpretation.
4. Estimate the number of stuffed animals the company would produce if it had 21 workers.
5. The company is considering hiring 10 more workers. Would it be reasonable to use the same technique as in the previous question to predict how the production would change? Why or why not?