$($Related to Checkpoint $18\mathrm{.}2)($Calculating the cash conversion cycle$)$ Network Solutions just introduced a new, fully automated manufacturing plant that produces $2,000$

wireless routers per day with materials costs of $$45$ per router and no other costs. The average number of days a router is held in inventory before being sold is $45$ days.

In addition, they generally pay their suppliers in $24$ days, while collecting from their customers after $21$ days.

a$.$ What is the cash conversion cycle?

b$.$ What would happen to the cash conversion cycle if they could stretch their payments to suppliers from $24$ days to $44$ days?

c$.$ How much would working capital be reduced if they stretched their payments to suppliers from $24$ days to $44$ days?