Anne Teak, the financial manager of a furniture manufacturer, is considering operating a lock$-$box system. She forecasts that $900$ payments a day will be made to lock boxes with an average payment size of $$2,500.$ The bank$$s charge f

$1.$ If the lock box makes the cash available $2$ days earlier, calculate the net daily advantage of the system.

Note: Do not round intermediate calculations.

$2.$ Is it worthwhile to adopt the system?

$3.$ 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 intermediate calculations. Round your answer to $2$ decimal places.