SOLUTION: Worker Efficiency: In a study pf worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker t hours after starting

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Question 201851: Worker Efficiency: In a study pf worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled by the formula
N (t) = -3r3 + 23r2 + 8t
A. Rewrite the formula by factoring the right-hand side completly
B. Use the factored version of the formula to find N(3)
c. Use the accompanying graph to estimate the time at which workers are most efficient.
d. Use the accompanying graph to estimate the maximum number of components assembled per hour during an 8-hr shift.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Somehow you've got your independent variables a little muddled. I think that the independent variable is t (for time) and not r, as you have it! So, let's start with...
N%28t%29+=+-3t%5E3%2B23t%5E2%2B8t and this represents the number of components assembled per hour by the average worker t hours after starting work.
A. The factored form is:
N%28t%29+=+t%283t%2B1%29%28-t%2B8%29
B. Find N%283%29 using the factored form. Substitute t = 3.
N%283%29+=+3%283%283%29%2B1%29%28-3%2B8%29 Evaluate.
N%283%29+=+3%289%2B1%29%285%29
highlight%28N%283%29+=+150%29 Components per hour 3 hours after starting work.
The graph of N%28t%29 is:
graph%28400%2C400%2C-5%2C10%2C-5%2C250%2C-3x%5E3%2B23x%5E2%2B8x%29
C. The estimated time, t, at which the workers are most efficient is t = 5, or 5 hours after starting work.
D. From the graph, it can be estimated that the maximum number of components assembled per hour during an eight-hour shift is 242.
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