Investing 50 gold a day should net you somewhere around 80 to 100 gold in profit. The investing would probably take an hour, the selling a day, and then you would have to cancel/relist items, add new buy orders, etc for an hour the following day.
So every other day you would earn approximately 40 gold. At a pace of 40 gold per day, assuming your income is not scaling (it should be), then you'll need to spend 45 hours during 45 days to purchase a 1800 gold legendary.
The trick to saving up for a legendary is not in grunt work, but rather, scaling your trading post methods. How can you scale up your business? The easiest way is to diversify among similar markets that are already working for you. With the case of fast moving crafting materials, you can often just invest more.
Through a combination of investing more as well as in additional but similar markets to what you already have working, you can scale your profits to greater heights. It then becomes possible to invest your profits instead of just the same seed money over and over again. Instead of 40 gold profit, you'll grow to 60, 100, 200, etc over time. It's not unreasonable to go from 50 gold to 150 in a single week, then 400-600 by the next.
Learn to make decent profits consistently from the same investment. Then scale your business.
In comparison to 45 days, how long did it take you to get your own legendary (assuming you have one already)? Are you currently trying to save for one now? What's your plan?