Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in dollars) given by S′(t) = 150 - t², where t is the number of years of operation of the machine, while producing a rate of annual costs (in dollars) of

(a) For how many years will it be profitable to use this new machine?
(b) What are the net total savings during the first year of use of the machine?
(c) What are the net total savings over the entire period of use of the machine?

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11 C' (t) = 1² + = t. 4