Problem $2-8($Algo$)$

A property title search firm is contemplating using online software to increase the productivity of the researcher performing the search. Currently, an average of $62$ minutes is needed to do a title search. The researcher cost is $$2\mathrm{.}00$ per minute. Clients are charged a fee of $$450.$ Company A$\text{'}$s software would reduce the average search time by $17$ minutes, at a cost of $$4\mathrm{.}00$ per search. Company B$\text{'}$s software would reduce the average search time by $22$ minutes at a cost of $$6\mathrm{.}00$ per search.