P$15-13$ Lockbox system Eagle Industries feels that a lockbox system can shorten its accounts receivable collection period by $3$ days. Credit sales are $$3,240,000$ per year, billed on a continuous basis. The firm has other equally risky investments with a return of $15\%.$ The cost of the lockbox system is $$9,000$ per year. $($Note: Assume a $365-$day year.$)$

a$)$ What amount of cash will be made available for other uses under the lockbox system?

b$)$ What net benefit $($cost$)$ will the firm realize if it adopts the lockbox system? Should it adopt the proposed lockbox system?

Please show all the work on how you arrive at the answer, thank you.