SOLUTION: In a study of worker efficiency at Wong Lab, it was found that the number of components assembled per hour by the average worker (t) hours afteree starting work could be modeled by

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Question 141598: In a study of worker efficiency at Wong Lab, it was found that the number of components assembled per hour by the average worker (t) hours afteree starting work could be modeled by the formula.
N(t)=-3t^3+23t^2+8t
a)Rewrite the formula by factoring the right-hand side completely.
b) Use the factored version of the formula to find N(3)
c) Use the accompanying graph to estimate the time at which the workers are most efficient.
d) Use the accompanying graph to estimate the maximum number of components assembled per hour during an 8-hour shift.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a study of worker efficiency at Wong Lab, 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)=-3t^3+23t^2+8t
;
a)Rewrite the formula by factoring the right-hand side completely.
Factor out -t:
N(t) = -t(+3t^2 - 23t - 8)
Factors to:
N(t) = -t(3t + 1)(t - 8)
:
b) Use the factored version of the formula to find N(3)
N(3) = -3(3(3) +1) (3 - 8)
N(3) = -3(10)(-5)
N(3) = +150 components per hr, after 3 hrs; per worker
:
+graph%28+300%2C+200%2C+-4%2C+10%2C+-100%2C+300%2C+-3x%5E3%2B23x%5E2%2B8x%29+
c) Use the accompanying graph to estimate the time at which the workers are most efficient.
Looks like about 5.25 hrs
;
d) Use the accompanying graph to estimate the maximum number of components assembled per hour during an 8-hour shift.
Looks like about 240 units