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) = -3t3 + 23t2 + 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.