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As for animal products, definitely process all the gold/iridium starred goods, as you don't get as many eggs/milk/wool in one day as you do produce and it's a nice little swell in your bank
If you really want to dig into the math, this might be a good place to start:
https://stardewvalleywiki.com/Preserves_Jar_Productivity
So *if* you've built your preserving operation having done the math to ensure that you have enough jars to preserve everything you produce, then you *should*. There's little reason not to.
For instance: A deluxe barn can hold 136 jars. The jars cycle every 2-3 days (Depending on how early you go to bed), but generally you can assume a new batch of preserves every 3 days (Because you're probably not going back to bed before noon). That means you'll have 9.3 batches per season. Which means you can process 1269 units of produce per season, with that one deluxe barn.
So if you're in spring and wanting to plant, say, Rhubarb--which is a very good choice for preserving--you'll get two crops per season. If you planted 635 or so rhubarb, then you should put every rhubarb you harvest into the jars, because that's exactly the right number to keep up with your entire season's production.
If you planted more than that, then you may want to sell the gold star stuff, as long as you keep 635 units from each of your two harvests that season for preserving.
However, another concern is that you may actually want to grow enough produce to maintain a surplus above and beyond what your jars can process.
The reasons you'd do this are obviously:
1. Winter, when you can't grow anything, if you have a surplus from the rest of the year, you can keep your jars running through the winter and keep that income stream reliable. You're not suffering the opportunity cost of idle jars.
2. Even in a growing season, you'll have some lag time before your first harvest comes in, and you'll want enough leftover from last season to keep the jars running until then.
Now, our previous example took this into account somewhat, as rhubarb is a 13 day grow time product, so you'd harvest on the 13th, and the 26th. Our previous figure of 1269.3 units processed per season is assuming we start the jars working on the 1st day of the season, but we wouldn't have had produce to put in them until the 13th. So what we produced in Spring is probably enough to keep the jars working until we can get a crop of say, melons, harvested on the 12th or so of Summer.
But let's say we're apparently out of our damn minds and chose to plant parsnips. This is a 7 harvest per season crop, so we only have to plant 182 parsnips to keep our jars active all month, IF we always harvest and replant immediately, each time the crop comes in every 4 days.
But what this means is that if we grow parsnips in Spring, and melons in Summer, we're going to end up with 8 days in Summer where our jars are idle. At minimum. And this sucks.
So we might want to plant a few more parsnips. 8-10 days is 2-3 work cycles for the jars, so we'd want an extra 272-408 parsnips over the course of the season. Let's play it safe and choose 408, because we're too lazy to figure *exactly* how many extra we'll need. Since you're getting 7 crops of parsnips over the Spring, we'll divide 408 by 7 and determine we need 58.3 additional parsnips planted, each planting day. So instead of 182 parsnips, we're buying and planting 240.3, or 241 because you can't plant a third of a parsnip.
Of course, if you're wanting to keep producing preserves straight through Winter, then you're going to need an entire season's worth of surplus. Which means you need to build up an extra 1270 units of produce over the course of Spring, Summer, and Fall. Collectively, not 1270 extra from each of them.
With the first example of Rhubarb in Spring, you could hit this target by doubling the planting, so 1270 units planted each time. This would mean you've already hit your yearly surplus target by the end of Spring. But that's a lot of Rhubarb to plant.
Alternatively, you might choose a higher yield crop to make up the surplus. For instance, take blueberries (Please, take some, I'm drowning in them). Blueberries take 13 days to grow (Which can be shortened to 10 with Deluxe Speed-Gro), and then produce a crop every 4 days thereafter. This produces 3 crops, or 4 if you used Speed-Gro (Even normal Speed-Gro would net you that one last harvest). And, terrifyingly, each plant produces THREE berries at harvest. 2% of them will actually produce even more than three.
So if you planted 635 rhubarb in spring, and you reuse the plots for blueberries in Summer, you'd get 7620(!!!) blueberries by the end of Summer. This obviously completely swamps and overwhelms your preserve production capability, so you will definitely have enough units to continue production through Winter. And you should probably sell all the silver and gold star ones immediately, because oh my god that's a lot of blueberries.
Alternatively, you might choose Hot Peppers, which, with the same 635 planted, would yield you 4445 units over the course of the season, and not swamp you quite as badly. On the other hand, you'd make less money overall, because blueberries are higher profit per day. You could, of course, also choose to *not* re-use all 635 planting spots you so laboriously hoed up back in Spring, but then they're probably going to return to being normal dirt, and you'll have to re-hoe them in Autumn, or whatever, and who wants to do that?
Realistically though, you'll probably plant Starfruit, and get no surplus from 635 units planted. But you can make it up with cranberries or grapes in Fall. I'd only recommend graps (Or *anything* that grows on a trellis) if you've already got Junimo Huts though, because they're a pain to harvest otherwise, and end up taking up a ton of space because you can only plant them with two rows being contiguous, as you need space to walk between.
If not, then sure, sell some.
But personally I design my farm with the math in mind. Generally I'm going to have somewhere around 384 crop plots outside the greenhouse, and the usual 116 inside. Which means I only bother to make 116 kegs, and only upgrade the winery barn once, because you can fit exactly 116 kegs into the Big Barn.
384 crop plots outside is because that's what the optimal Junimo Hut + 8 Iridium Sprinklers layout will allow, if you can squeeze two of those blocks into your farm layout, which is admittedly only possible on the standard farm map... None of the other official layouts have sufficient contiguous space so you're going to have to make compromises if you're playing on forest, or riverlands, or wilderness, or hilltop.
But knowing that, it lets me choose what seeds I buy, so that my crops are just keeping up with, or slightly outpacing, my one single deluxe barn full of preserve jars.
And then the rest of my farm's space can be dedicated to a barn and a couple coops and the rather huge amount of tall grass required to feed 36 animals.
If you'd rather skip the animals, you'd probably make more money by installing a second barn full of preserve jars or kegs and dedicating the rest of the land to farming crops as well, though this tends to make for an ugly farm layout, IMO.
I mean, the *highest* profit comes by making absolutely nothing but wine, but that's a bit boring, and your profits are going to tend to dwindle during Winter when only your greenhouse can keep running, and that only gives you enough Ancient Fruit to run 116 kegs.
Also, if you want to make anything other than Ancient Fruit wine, you're going to want Junimos because you're going to want grapes in Autumn, and possibly hops in summer. Both of which are trellis crops which are a pain in the butt to manage without Junimo huts, and because you have to harvest hops *every day*, which is a huge time sink without the automation.