It takes Blitz Inc., about five days to receive and deposit checks from customers. The company's management is considering a lockbox system to reduce the firm $\text{'}$s collection times. It is expected that the lockbox system will reduce receipt and deposit times to three days total. Average daily collections are $$141,900$ and the required rate of return is an EAR of $7$ percent.

a$.$ What is the reduction in outstanding cash balance as a result of implementing the lockbox system? $(6$ marks$)$

b$.$ What is the dollar return $($daily dollar return$)$ that could be earned on these savings? $(8$ marks$)$

c$.$ Explain how a lockbox system operates and why a firm might consider implementing such a system. $(6$ marks$)$