A property title search firm is contemplating using online software to increase the productivity of the researcher performing the search.

Currently, an average of $65$ minutes is needed to do a title search. The researcher cost is $$1\mathrm{.}70$ per minute. Clients are charged a fee

of $$420.$ Company A$\text{'}$s software would reduce the average search time by $16$ minutes, at a cost of $$3\mathrm{.}70$ per search. Company B$\text{'}$s

software would reduce the average search time by $21$ minutes at a cost of $$5\mathrm{.}70$ per search.

a$.$ Calculate the productivity in terms of revenue per dollar of input. $($Round your intermediate calculations and final answers to $2$

decimal places.$)$