A local factory has hired you to structure their network into small LANs. The factory consists of three main departments: design, administration and sales. You are given: four switches each with $24$ ports $($Fa$0/1$ Fa$0/24),$ one router with $7$ interfaces $($G$0/0$ G$0/6),$ an ISP via a phone modem, all the necessary cabling and a $192\mathrm{.}168\mathrm{.}0\mathrm{.}0/23$ address space assigned by the ISP. You are asked to assign the last usable IP address in any of the small LANs to the default gateway of that LAN.

Initially, only the design and administration departments should be networked. The design department needs to cater for $8$ desktop PCs and is not expected to grow beyond $14$; the admin department has $3$ desktop PCs and one network printer and is not expected to grow in size in the future.

$($a$)$ Partition the IP address space provided and assign two subnets for the design LAN and the admin LAN. Provide for each subnet: the subnet address, the subnet mask, the first and the last addresses assigned to the end devices, and the default gateway address.