I take it that your company "owns" the domain name dilgardfoods.com, so you
can point that "name" to any public IP address, including IP addresses
assigned to gateways/routers/firewalls (at your office or at a data center
of your choice).
Your company's internal LAN will use "private" addresses as follows -
assuming standards for IP 4:
10.xxx.xxx.xxx or 172.16.xxx.xxx or 192.168.xxx.xxx
All other addresses are "public" addresses (reserved for the Internet).
Network gateways/routers/firewalls map public IP addresses to private IP
addresses. You just configure the gateway, etc. Your public IP address will
be assigned by your ISP. Your LAN administrator will assign a private IP
address to the gateway, and most likely configure it to assign addresses
(dynamic or static) to other devices on you LAN.
No, your LAN is not in the data center. But the data center provider could
offer a VPN account to connect to THEIR LAN.