DHCP is based on a "DORA" (Discover-Offer-Request-Accept) protocol; Minimally the Discover packets are broadcasted on a MAC domain by the booting clients searching for a DHCP server. Broadcast traffic is by default blocked by routers, then normally you will not be able to boot PXE clients on network 172.16.87.xxx out of a DHCP server located at 198.19.99.xxx.
But you can enable at the router "linking" both networks a DHCP relay agent (IP Helper) this way the router will take the broadcast request coming from the client at 172.16.87.xxx network and it will uni-cast the request over the DHCP server in the 198.19.99.xxx network.
The routers (not the networks) provide the DHCP relay services. You do not need anything else at the destination. TFTP traffic does not need to be relayed.