Anne Teak, the financial manager of a furniture manufacturer, is considering operating a lock$-$box system. She forecasts that $400$

payments a day will be made to lock boxes with an average payment size of $$3,000.$ The bank's charge for operating the lock boxes is

$$0\mathrm{.}40$ a check. The interest rate is $0\mathrm{.}011\%$ per day.

a$.$ If the lock box makes the cash available $2$ days earlier, calculate the net daily advantage of the system.

Note: Do not round Intermedlate colculations.

b$.$ Is it worthwhile to adopt the system?

c$.$ What minimum reduction in the time to collect and process each check is needed to justify use of the lock$-$box system?

Note: Do not round Intermedlate calculations. Round your answer to $2$ decimal places.

Answer is complete but not entirely correct.