Neon Light Company of Kansas City ships lamps and lighting appliances throughout the country. Ms$.$ Neon has determined that through the establishment of local collection centers around the country, she can speed up the collection of payments by two and one$-$half days. Furthermore, the cash management department of her bank has indicated to her that she can defer her payments on her accounts by one$-$half day without affecting suppliers. The bank has a remote disbursement center in Florida.

If Neon Light Company has $$3\mathrm{.}10$ million per day in collections and $$1\mathrm{.}22$ million per day in disbursements, how many dollars will the cash management system free up$?$

Note: Enter your answer in dollars not in millions $($e$.$g$.,$ $$1,234,567).$

If Neon Light Company can earn $6$ percent per annum on freed$-$up funds, how much will the income be$?$

Note: Enter your answer in dollars not in millions $($e$.$g$.,$ $$1,234,567).$

If the total cost of the new system is $$485,000,$ should it be implemented?