I have not only used linear programming in the industry, I have also had to write my own solver because the existing ones (even commercial) were to slow. (This was possible only because I only cares about a very approximate solution)
The triangulations you mention are important in the current group I'm working in.
I'm curious to hear what you specifically use these algorithms for!
PS: My point is not that these things are never used, they clearly are, I'm saying that the majority of CPU cycles globally goes towards "idle", then pushing pixels around with simple bitblt-like algorithms for 2D graphics, then whatever it is that browsers do on the inside, then operating system internals, and then specialised and more interesting algorithms like Linear Programming are a vanishingly small slice of whatever is left of that pie chart.
The triangulations you mention are important in the current group I'm working in.