Can't tell you. Don't work there any more and don't remember in detail, but wouldn't disclose that if I was still there. Let's say: a significant fraction of an engineer per year. (But note that this was a very large internet company, worth tens of billions, to have had to build it's own multi level load balancer, not a startup.)
You can't spend money on haproxy license. It's free. They make money by selling appliances (servers with haproxy pre installed).
Nginx however is $1900 per year per server. There are plenty of critical features missing from the free edition, for example the status page to see available servers or metrics exporting for monitoring.
Just to do justice to my coworkers working on the ALOHA appliance, it's not just a "server with haproxy preinstalled" but a tight integration of haproxy plus a few management tools into a dedicated distro built from scratch and packaged as an upgradable image like you'd have on your routers or switches. The whole OS image is around 16 megabytes, kernel included, and it contains a 10 Gbps-capable anti-ddos module, a web interface, and troubleshooting tools. And of course you have root access on it and it doesn't void your support to start to hack on it (not pointing the finger at anyone, but still a little bit :-))