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

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Question 263217: Worker efficiency. In a study of 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)=-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) (Show Source):
You can put this solution on YOUR website!
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)=-3t^3 + 23t^2 +8t.
:
a) Rewrite the formula by factoring the right-hand side
completely.
n(t) = -3t^3 + 23t^2 + 8t
factor out -t, changing signs makes it easier to factor
n(t) = -t(3t^2 - 23t - 8)
n(t) = -t(3t + 1)(t - 8)
:
b) Use the factored version of the formula to find N(3).
n(t) = -t(3t + 1)(t - 8)
n(3) = -3(3(3) + 1)(3 - 8)
n(3) = -3(10)(-5)
n(3) = +150 units
:
c) Use the accompanying graph to estimate the time at
which the workers are most efficient.

Looks to be about 5.25 hrs, wouldn't you think?
:
d) Use the accompanying graph to estimate the
maximum number of components assembled per
hour during an 8-hour shift.
:
at 5.25 hrs it looks like 250 units per hr, however we can calculate that
n(t) = -t(3t + 1)(t - 8)
n(5.25) = -5.25(3(5.25) + 1)(5.25-8)
n(5.25) = -5.25(16.75)(-2.75)
n(5.25) = 241.8 ~ 240 units/hr would be closer