Rationale for 254 ppi pixel density on M-series MBP's?

[mr_roboto]

The engineering is determined in the panel fabs belonging to companies like BOE, and actually has very little to do with Apple or OS-X. It's far more likely that it has something to do with the intricacies of the LCD production process, rather than Apple specifying they wanted exactly 254 ppi.

Judging by the job listings I've seen over the years, Apple does much more LCD panel engineering in-house than you seem to think.

Apple's notorious for cutting deals with suppliers along the lines of "we will underwrite creating a new plant or manufacturing line in return for concessions X Y and Z". When you're making that kind of deal, you get exactly what you want, as long as it's manufacturable - if Apple's special LCD design needs extra process steps or equipment, well, Apple's paying for it.

Also I'm not sure why you think specifying an exact desired PPI would be a hard ask for a LCD panel manufacturer even without the "special" relationships Apple builds with suppliers. Going ultra high res is hard, but a minor change like 220->254 shouldn't be a big deal.

 

[quarkysg]

You want to think about this like a hardware engineer or scientist, since they're likely the ones that made the selection. They knew there would be no significant functional difference between setting the default UI density to 126 or 128 ppi (or some other nearby number) rather than 127.

IMHO, the simple answer could be that 127 is exactly 7 bits and it probably made it easier and faster for computation. This likely started from the original Mac days, and back then, memory and CPU speed is limited. That it matches exactly to some metric measurement is likely a coincidence.

 

[theorist9]

I don't know why you mentioned me, since I ducked out of the thread after the numerology started up, but since you did, now you get me rambling again.

I mentioned you because you liked the post to which I was replying, indicating you were of like mind to the poster. Hence it seemed appropriate to reply to the both of you:

Apple first launched the Retina MacBook Pros with double-resolution displays to the 1440x900 displays they had been using. Then they decided to change the default "looks like" resolution to be one step up from the default ("looks like 1680x1050"). After a couple years of seeing how many users reverted back to "looks like 1440x900" and seeing how low that number was, when they had the opportunity to do the redesign for the M1, they sought out panels as close to that as they could so it would be a native 2x again with a similar amount of screen real estate per inch that they had in the previous MBP model. That's it.

Interesting that users reverted to 1440 x 900; this could have been a preference for the sharpness of integer scaling, rather than a UI size preference. How does Apple collect this info? Is it part of the anonymized analytics info. they ask you to share when you install a new OS?

There's no big master plan here, nothing hiding in the numbers.

Never said there was any "master plan"/DaVinci Code/gematria going on here! Don't know where you're getting that. [OK, maybe I briefly consulted with Marjorie Taylor Greene on this, but honestly, no other conspiracy theorists were involved.] I was simply pointing out that there was probably some reason they chose 127 ppi specifically, and I thought the fact that it works out to exactly 5 ppmm seemed a likely explanation.

 

[theorist9]

IMHO, the simple answer could be that 127 is exactly 7 bits and it probably made it easier and faster for computation. This likely started from the original Mac days, and back then, memory and CPU speed is limited. That it matches exactly to some metric measurement is likely a coincidence.

That's an interesting alternative explanation. But note that this was a change made in about 2016.

 

[leman]

IMHO, the simple answer could be that 127 is exactly 7 bits and it probably made it easier and faster for computation. This likely started from the original Mac days, and back then, memory and CPU speed is limited. That it matches exactly to some metric measurement is likely a coincidence.

Why would you need to compute along the metric of bits per inch? How would 7 bits in a completely irrelevant metric help you optimize performance? The earlier Macs had 72pixels per inch btw

 

[tornado99]

Judging by the job listings I've seen over the years, Apple does much more LCD panel engineering in-house than you seem to think.

Apple's notorious for cutting deals with suppliers along the lines of "we will underwrite creating a new plant or manufacturing line in return for concessions X Y and Z". When you're making that kind of deal, you get exactly what you want, as long as it's manufacturable - if Apple's special LCD design needs extra process steps or equipment, well, Apple's paying for it.

Also I'm not sure why you think specifying an exact desired PPI would be a hard ask for a LCD panel manufacturer even without the "special" relationships Apple builds with suppliers. Going ultra high res is hard, but a minor change like 220->254 shouldn't be a big deal.

From my understanding of lcd panel fabrication they tend to start with small sizes like 3 or 4", and if they can get stable epitaxial growth at a certain pixel density, they scale it up. So the 254 ppi probably comes as a by-product of whatever chemical process they were using.

 

[quarkysg]

Why would you need to compute along the metric of bits per inch? How would 7 bits in a completely irrelevant metric help you optimize performance? The earlier Macs had 72pixels per inch btw

Well, the screen may be 72 pixels but the internal canvas may still be 127 points. The thing is only Apple knows. And during the 68000 days, any savings in arithmetic cost will be good. We can only speculate here.

 

[leman]

Well, the screen may be 72 pixels but the internal canvas may still be 127 points. The thing is only Apple knows. And during the 68000 days, any savings in arithmetic cost will be good. We can only speculate here.

But why would you do arithmetics on PPI? When drawing, you do operations on coordinates. PPI doesn’t matter at all.

 

[MajorFubar]

I'm reading through all this and remembering I'm of an age where my first computer's high-res graphics mode was 256x192 in monochrome and I thought it was phenomenal.

Please ignore me and carry on.

 

[mr_roboto]

From my understanding of lcd panel fabrication they tend to start with small sizes like 3 or 4", and if they can get stable epitaxial growth at a certain pixel density, they scale it up. So the 254 ppi probably comes as a by-product of whatever chemical process they were using.

I think you have one or more fundamental misunderstandings here.

Epitaxy is the process of growing a uniform crystalline film of some material on top of a surface. It is not how you create the features which define pixel pitch in a LCD, such as transistors, wires, and electrodes. Those are printed into thin films (some of which may be deposited by epitaxy) using a lithographic process in which artwork is transferred from a mask to the surface.

For example, the basics of photolithography: You frequently start with a thin film already deposited on the surface, such as a metal material for creating wires. But deposition left you with just a uniform featureless film, so you need to etch away the parts of the film which aren't the wire pattern you want. You deposit a uniform layer of photoresist on top of the metal, pattern the photoresist by shining high intensity light through a mask, etch the resulting pattern in the photoresist using chemicals which only attack the exposed (or only the not-exposed) parts of the photoresist, and finally finish off with a different chemical to etch the exposed metal while leaving the metal still covered by photoresist alone.

So feature size in IC manufacturing and pixel density in LCDs isn't an emergent property of chemical processes, it's just the size of patterns in masks, and the masks are manufactured to have exactly the artwork you want.

 

[tornado99]

I think you have one or more fundamental misunderstandings here.

Epitaxy is the process of growing a uniform crystalline film of some material on top of a surface. It is not how you create the features which define pixel pitch in a LCD, such as transistors, wires, and electrodes. Those are printed into thin films (some of which may be deposited by epitaxy) using a lithographic process in which artwork is transferred from a mask to the surface.

For example, the basics of photolithography: You frequently start with a thin film already deposited on the surface, such as a metal material for creating wires. But deposition left you with just a uniform featureless film, so you need to etch away the parts of the film which aren't the wire pattern you want. You deposit a uniform layer of photoresist on top of the metal, pattern the photoresist by shining high intensity light through a mask, etch the resulting pattern in the photoresist using chemicals which only attack the exposed (or only the not-exposed) parts of the photoresist, and finally finish off with a different chemical to etch the exposed metal while leaving the metal still covered by photoresist alone.

So feature size in IC manufacturing and pixel density in LCDs isn't an emergent property of chemical processes, it's just the size of patterns in masks, and the masks are manufactured to have exactly the artwork you want.

Sorry, you are mistaken. For example, from this review article discussing current manufacturing challenges actually epitaxial wafer defect requirement does depend on pixel pitch:

For differ-
ent applications, the specifications of defects in the epitaxial
wafer are different. For example, the defect size is 1 μm for
a 5.8′′ 2560 × 1440 resolution (QHD) smartphone, while the
defect size is around 3 μm for 55′′ 3840 × 2160 resolution 4K
TV​

There are many other challenges too in manufacturing a large pixel dense display. You can't just choose what you want and pop out a lcd panel at your desired ppi.

 

[Krevnik]

Interesting that users reverted to 1440 x 900; this could have been a preference for the sharpness of integer scaling, rather than a UI size preference. How does Apple collect this info? Is it part of the anonymized analytics info. they ask you to share when you install a new OS?

The discussion on this change exists on this forum and others, I linked to an article that talked about the change and how you can revert to the old behavior in 2016.

I can't confirm if Apple monitors this specific setting or not. But if they aren't, they are bad at analytics, so I think it's fair to assume they do watch these things to make better decisions going forward. When I worked on a particular large project, we used analytics to tell if a change we made was better for users or not. Things we wanted to know was:

- Is a feature gaining traction in the user base? Are users being successful or not when using the feature?
- If I make a change, how does that impact things? Are users more successful, or less? If the change is a preference/setting default, are users accepting the change, or reverting it?
- If I have two ways I can make a change, what if I ship both and see which one users have better luck with? (A/B testing)

That said, these sort of analytics can be malicious as well. "Does this change get people staying on Facebook for more or less time?" is very different IMO than "Does this change mean that people can style their presentation successfully in fewer steps?"

Never said there was any "master plan"/DaVinci Code/gematria going on here! Don't know where you're getting that. [OK, maybe I briefly consulted with Marjorie Taylor Greene on this, but honestly, no other conspiracy theorists were involved.] I was simply pointing out that there was probably some reason they chose 127 ppi specifically, and I thought the fact that it works out to exactly 5 ppmm seemed a likely explanation.

What I'm saying is that there was no mathing this out, or logic. We've probably spent more time on this thread than the engineers did on picking the resolution. Apple just wanted something close enough to the scaled resolution they were using, but would also work well with the mini-LED backlight array.

 

[theorist9]

The discussion on this change exists on this forum and others, I linked to an article that talked about the change and how you can revert to the old behavior in 2016.

I can't confirm if Apple monitors this specific setting or not. But if they aren't, they are bad at analytics, so I think it's fair to assume they do watch these things to make better decisions going forward. When I worked on a particular large project, we used analytics to tell if a change we made was better for users or not. Things we wanted to know was:

- Is a feature gaining traction in the user base? Are users being successful or not when using the feature?
- If I make a change, how does that impact things? Are users more successful, or less? If the change is a preference/setting default, are users accepting the change, or reverting it?
- If I have two ways I can make a change, what if I ship both and see which one users have better luck with? (A/B testing)

The limitation of just having the analytics, if you haven't also polled users, is you don't know why they've changed. Users could have reverted to 1440 x 900 either because they liked the sharper image from integer scaling, or because they liked the larger UI, or both. Without knowing this, you don't know how to make use of the data. I wonder if Apple polled users on this.

What I'm saying is that there was no mathing this out, or logic. We've probably spent more time on this thread than the engineers did on picking the resolution. Apple just wanted something close enough to the scaled resolution they were using, but would also work well with the mini-LED backlight array.

I'm saying there was likely no mathing this out as well. If I'm an engineer, and I'm thinking of increasing the default ppi from 110 to some number around 130, and the exact number isn't important, I'm going to pick 130. I'm not going to pick 127. So the fact that they picked a seemingly quirky number like 127 is likely because they were thinking metrically rather than imperially, because metrically that 127 ppi is 5 ppmm. The explanation is likely as simple as that.

 

[SpotOnT]

OK, I think I have it: There's TWO STEPS here.

For the first step, the Mac needs to convert its internal bitmap (127 pts/in) to the native resolution of the display. If the display is 254 ppi, then that's ideal, because after doing integer upsampling to 254 ppi, no non-integer downsampling is needed (the latter would, by contrast be needed with, say, a 218 ppi display). Question: How much effect does this have on quality?

Since I don't know the proper term of art, let's call the output from step one the "external bitmap", which is now in ppi

For the second step, the Mac needs to take the external bitmap and apply it to the display. If the user wishes the actual sizing to correspond to some integer fraction of the resolution of the display, that's ideal, because no non-integer scaling is needed.

In summary, there are two potential sources of artifacts:
Type 1: Those incurred in going from the 127 pts/in internal bitmap to a display whose native resolution is not an integer multiple of this.
Type 2: Those incurred in displaying the output of step 1 at a non-integer fraction of the native resolution of the display ("non-integer scaling").

Thus:
254 ppi display used at integer scaling: No Type 1 or Type 2 artifacts
254 ppi display used at non-integer scaling: Type 2 artifacts only.
220 ppi display used at integer scaling: Type 1 artifacts only.
220 ppi display used at non-integer scaling: Type 1 and Type 2 artifacts.

But this still leaves the question—why 127 ppi in the first place? Given that their early LCD monitors were typically ~100-110 ppi, wouldn't one of those resolutions have made more sense (so they could avoid the Type 1 artifacts for such displays)?

I think that is a really good summation.

My Macbook Pros from 2011 and 2012 both had 127 ppi screens. They are 1680-by-1050 on a 15.4” display. Why 127 rather than 110. Probably so you could fit more work on the screen? Nothing looks too small on my old MBP. Probably someone at Apple design just though it was the right “looks like” size for them or something.

Edit: Been reading this thread slowly, and chronologically. Just got to your 5 mm comment. That seems entirely plausible to me too! At the same time though, it is worth noting the 1680-1050 resolution was originally offered as an optional upgrade and sold alongside lower resolution MBP option. It could just have been a "lets cram more space on there" decision.

 

[Krevnik]

The limitation of just having the analytics, if you haven't also polled users, is you don't know why they've changed. Users could have reverted to 1440 x 900 either because they liked the sharper image from integer scaling, or because they liked the larger UI, or both. Without knowing this, you don't know how to make use of the data. I wonder if Apple polled users on this.

They likely have focus groups as well, but analytics are useful for teasing out patterns in larger populations than focus groups alone will give you.

I'm saying there was likely no mathing this out as well. If I'm an engineer, and I'm thinking of increasing the default ppi from 110 to some number around 130, and the exact number isn't important, I'm going to pick 130. I'm not going to pick 127. So the fact that they picked a seemingly quirky number like 127 is likely because they were thinking metrically rather than imperially, because metrically that 127 ppi is 5 ppmm. The explanation is likely as simple as that.

They didn't pick "127", that's my whole point. They picked "1680x1050 @ 15.4 inches". The final pixel density is an artifact of that previous decision, not a decision onto itself.

 

[mr_roboto]

Sorry, you are mistaken. For example, from this review article discussing current manufacturing challenges actually epitaxial wafer defect requirement does depend on pixel pitch:



There are many other challenges too in manufacturing a large pixel dense display. You can't just choose what you want and pop out a lcd panel at your desired ppi.

I don't think you are understanding the things you're googling very well.

The words you quoted at me only say that the maximum acceptable defect size in epitaxial films depends on the size of the patterns (e.g. pixel structures) you want to print on these films. This does not support your claim that there's some magic property of epitaxy (or other processes) which channeled Apple into the number 254.

The way things actually work is that first, a company like Apple asks for a a panel spec of Z ppi, dimensions X mm * Y mm. The LCD manufacturer then looks at defect density and defect size statistics for their manufacturing processes in each layer of the stackup (not just epitaxy) and comes back with a predicted scrap rate. That figure becomes part of the negotiating process on price and so forth.

At no point is there any difficulty with hitting exactly the PPI figure the customer wants. Forming features in chip/LCD manufacturing is fundamentally a high tech printing process, and like any other type of printing, the feature size of the artwork is easily and arbitrarily controllable within the resolution limits of the printing process.

 

[theorist9]

They didn't pick "127", that's my whole point. They picked "1680x1050 @ 15.4 inches". The final pixel density is an artifact of that previous decision, not a decision onto itself.

Except 1680x1050 @ 15.4 inches isn't 127 ppi, it's 129. Besides, as you said yourself, Apple didn't need an exact match to this, they "just wanted something close enough to the scaled resolution they were using". So if I'm an engineer, and I just want something close enough, I'm not going to pick 127 or 129, I'm going to pick 130—but only if I'm thinking in those units. If I'm instead thinking in terms of pixel pitch, which is typically expressed metrically, the obvious "close enough" pick is 200 microns, which just happens to be 127 ppi.

I think we may be having a communication failure....

 

[tornado99]

I don't think you are understanding the things you're googling very well.

The words you quoted at me only say that the maximum acceptable defect size in epitaxial films depends on the size of the patterns (e.g. pixel structures) you want to print on these films. This does not support your claim that there's some magic property of epitaxy (or other processes) which channeled Apple into the number 254.

The way things actually work is that first, a company like Apple asks for a a panel spec of Z ppi, dimensions X mm * Y mm. The LCD manufacturer then looks at defect density and defect size statistics for their manufacturing processes in each layer of the stackup (not just epitaxy) and comes back with a predicted scrap rate. That figure becomes part of the negotiating process on price and so forth.

At no point is there any difficulty with hitting exactly the PPI figure the customer wants. Forming features in chip/LCD manufacturing is fundamentally a high tech printing process, and like any other type of printing, the feature size of the artwork is easily and arbitrarily controllable within the resolution limits of the printing process.

I think you missed my point. You can't just pick any number and tell the LCD manufacturer to make that density. At some point the chemical processes fail. It's not just a matter of economics and yield. Otherwise where's the 500 ppi displays? Medical and industrial users will pay any price, but there's a limit even for them. It's not my field, but I have enough of a scientific background to understand the gist of the research I was quoting.

 

[theorist9]

I think you missed my point. You can't just pick any number and tell the LCD manufacturer to make that density. At some point the chemical processes fail. It's not just a matter of economics and yield. Otherwise where's the 500 ppi displays? Medical and industrial users will pay any price, but there's a limit even for them. It's not my field, but I have enough of a scientific background to understand the gist of the research I was quoting.

You're doing the same thing with @mr_roboto that you did with me. The discussion at hand wasn't about whether Apple could obtain *any* pixel density, no matter how high. Of course they can't, and no one was saying they could.

Rather, it was about whether Apple could request any *specific* pixel density they wished (so long as it wasn't so high that it exceeded current manufacturing capabilities).

You said no—that the LCD manufacturing process constrains panels to specific pixel densities. Thus by your argument, the 254 ppi on Apple's MBP's, and the 280 ppi on Dell's 31.5" 8k, result from inherent properties of LCD manufacturing, rather than specifications supplied by Apple and Dell, respectively:

The engineering is determined in the panel fabs belonging to companies like BOE, and actually has very little to do with Apple or OS-X. It's far more likely that it has something to do with the intricacies of the LCD production process, rather than Apple specifying they wanted exactly 254 ppi.

mr_roboto explained that's incorrect. The pixel densities are determined by etching, and the etch size is selectable. Thus Apple can choose whatever ppi they wished (up to the maximum available with current tech):

The words you quoted at me only say that the maximum acceptable defect size in epitaxial films depends on the size of the patterns (e.g. pixel structures) you want to print on these films. This does not support your claim that there's some magic property of epitaxy (or other processes) which channeled Apple into the number 254.
....
At no point is there any difficulty with hitting exactly the PPI figure the customer wants. Forming features in chip/LCD manufacturing is fundamentally a high tech printing process, and like any other type of printing, the feature size of the artwork is easily and arbitrarily controllable within the resolution limits of the printing process.

Rather than acknowledging this, you're now pretending the argument was never about whether ppi's were selectable (which it was), and that @mr_roboto was instead arguing that any ppi could be manufactured (which he wasn't). This kind of game-playing is called a "straw man": You're ascribing to mr_roboto an absurd argument he never made, and arguing against that.

 

[tornado99]

What do you mean by "etch size"?

 

[theorist9]

What do you mean by "etch size"?

I'm referring to the pixel pitch in the etching used to create the panel:

How liquid crystal display (lcd) is made - material, manufacture, making, used, components, procedure, steps, machine

 

[tornado99]

The words you quoted at me only say that the maximum acceptable defect size in epitaxial films depends on the size of the patterns (e.g. pixel structures) you want to print on these films. This does not support your claim that there's some magic property of epitaxy (or other processes) which channeled Apple into the number 254.

Except I never actually said this. You seem to be playing the same game as @theorist9. I said that they probably started off with a small screen e.g. for a mobile phone of say 5" diagonal and some common resolution (which works out as 254 ppi). Apple then asked them to cut the master panel differently so instead of 20 phone screens you end up a with a few 14" screens instead.

 

[mr_roboto]

Except I never actually said this. You seem to be playing the same game as @theorist9. I said that they probably started off with a small screen e.g. for a mobile phone of say 5" diagonal and some common resolution (which works out as 254 ppi). Apple then asked them to cut the master panel differently so instead of 20 phone screens you end up a with a few 14" screens instead.

Amusingly we already discussed this idea earlier in the thread, when I misinterpreted someone else as saying what you've just said now.

If this isn't another misunderstanding, it's impossible to do what you describe. A piece of mother glass that has had TFT circuitry and subpixel electrodes designed for phone displays printed on it cannot be cut into fewer, bigger displays.

Even if that isn't what you meant, there's still a ton of problems with your ideas:

I think you missed my point. You can't just pick any number and tell the LCD manufacturer to make that density. At some point the chemical processes fail. It's not just a matter of economics and yield. Otherwise where's the 500 ppi displays? Medical and industrial users will pay any price, but there's a limit even for them. It's not my field, but I have enough of a scientific background to understand the gist of the research I was quoting.

Do you understand that very similar processes successfully manufacture chips with feature sizes measured in nanometers? The feature size required for 500ppi is not an obstacle. If LCD manufacturers can't hit it today, it's probably only because nobody has asked for it, and thus they haven't bothered investing in all the things pioneered in the semiconductor manufacturing world. (Better cleanroom requirements, higher materials purity, and so forth.)

More importantly, there's entirely different reasons not to try for 500ppi in laptop computer LCDs. I can easily come up with several off the top of my head:

* What's the reward for trying? It would be nice to have ~500ppi, but thanks to the limits of human eyes it's not nearly as important as the jump from ~125 to ~250 was. Diminishing returns.

* Another doubling of horizontal and vertical resolution means 4x the pixels, which means 4x the memory and ~4x the compute required to draw things. In battery powered devices, even the memory bandwidth required to refresh 4x the pixels can be a significant energy cost.

* Speaking of energy costs, an important limit on LCD backlight efficiency (the fraction of the photons emitted by the backlight which can actually make it to your eyes) is the size of the TFT transistor embedded in each subpixel. There are problems with scaling the size of these transistors down, since the transistor materials possible to use in LCDs aren't great.

As pixel pitch goes up, these transistors get bigger relative to the subpixel, and backlight efficiency goes down. This was one of the big reasons Apple took forever to bring Retina displays to the MacBook Air line - for a long time they couldn't reduce the power demands of other components enough to allocate more power to the display backlight.

Double the PPI again and this problem will only get worse.

Basically, you're barking up the wrong tree if you think the one and only thing keeping Apple from asking for 500ppi LCDs is the LCD manufacturing process.

 

[tornado99]

The feature size required for 500ppi is not an obstacle. If LCD manufacturers can't hit it today, it's probably only because nobody has asked for it,

So explain why the 27" 5K panels made by LG for the Ultrafine series had notoriously poor yield and quality control problems? I don't get why you think any density panel is possible simply if "people ask for it", when clearly large high density panels are difficult to manufacture.

* What's the reward for trying? It would be nice to have ~500ppi, but thanks to the limits of human eyes it's not nearly as important as the jump from ~125 to ~250 was. Diminishing returns.

@theorist9 , would disagree with you. They seem to be convinced that the limit of human vision is 500 or 1000 ppi, and they don't seem to acknowledge the diminishing returns argument which I also made.

 

[Krevnik]

Except 1680x1050 @ 15.4 inches isn't 127 ppi, it's 129. Besides, as you said yourself, Apple didn't need an exact match to this, they "just wanted something close enough to the scaled resolution they were using". So if I'm an engineer, and I just want something close enough, I'm not going to pick 127 or 129, I'm going to pick 130—but only if I'm thinking in those units. If I'm instead thinking in terms of pixel pitch, which is typically expressed metrically, the obvious "close enough" pick is 200 microns, which just happens to be 127 ppi.

I think we may be having a communication failure....

Honestly what I keep taking away from your arguments is that there must have been some motive for Apple to go with this density. And my simple answer is that there isn’t one that you will be able to point to that isn’t some variation of “this number seems special”. It isn’t a special number is really the crux of what I’m trying to get at, Apple didn’t do any big revisit here. Apologies if that’s not persuasive evidence, but it’s not like we can dig into the negotiations that Apple had with LG.

I did mention “~127” when I started replying. Yes, I know it isn’t exact, and it’s not 129 px/inch either, it’s 128.65 if we want to get really pedantic about it, putting the exacting display Apple would want at 257.12 px/inch.

Honestly, I imagine the discussion between LG and Apple going a bit like this (only more complicated, because contracts, etc):

Apple: Hey, LG, we need a panel that‘s roughly X px/inch for this display we are working on, what can you do?
LG: Well, we’ve got these options, and here’s what the yields will likely look like, and here’s the startup costs and per sheet costs for each since it’s not something we already do.
Apple: Option Y looks like a good balance, let’s do that.

I would be surprised if it was more complicated than “close enough, low enough startup costs”.