Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in dollars) given by the function S'(x), where x is the number of years of operation of the machine, while producing a rate of annual costs (in dollars) given by the function C'(x) S'(x) = 222 - x-, C' (x ) = x + 5x a. For how many years will it be profitable to use this new machine? The number of profitable years is b. What are the net total savings during the first year of use of the machine? The net total savings during the first year of use of the machine is $ (Round to the nearest dollar as needed.) c. What are the net total savings over the entire period of use of the machine? The net total savings over the entire period of use of the machine is $ (Round to the nearest dollar as needed.)