$($Related to Checkpoint $18\mathrm{.}2)($Calculating the cash conversion cycle$)$ Network Solutions just introduced a new, fully automated manufacturing plant that produces $3,000$ 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 $66$ days. In addition, they generally pay their

suppliers in $31$ days, while collecting from their customers after $20$ 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 $31$ days to $51$ days?

c$.$ How much would working capital be reduced if they stretched their payments to suppliers from $31$ days to $51$ days?

a$.$ The cash conversion cycle is $55$ days. $($Round to the nearest whole number.$)$

b$.$ If they could stretch their payments to suppliers from $31$ days to $51$ days, the cash conversion cycle would be

days. $($Round to the nearest whole number.$)$