How to optimize apple pressing This is how the press works: (I'm sorry if it looks like a Pokeball, but I'm proud of my paint)

This is a top view. The black part is the container, it is a hollow cylinder. In the middle (in dark blue), there is the bladder. It's made of rubber and in the bladder, we put water (light blue). The red represents the apples.
The principle is simple: you fill in the container with apples (they are already a bit crushed but nevermind). Then you close the container and you start sending water in the bladder which will get bigger and bigger, pressing the apples. Then the apple juice comes out through holes in the container. 
Now my question is, assuming we don't care about the amount of water & time used, does it give more apple juice (in proportion, not in quantity) to partially fill the bladder and then put less apples in the container or to entirely fill the container with apples and to put more pressure into the bladder?
What if we do care about water and time, is there an optimal process?
 A: This might be a better fit for the engineering site. 
Offhand I would say it should not matter. A simple model would be that an apple is like a sponge full of water. If you squeeze hard enough, you get essentially all of the water out. It shouldn't matter if the sponge is big or small. 
However, simple models aren't always accurate. And it isn't easy to come up with a better model unless you know more than I do about the mechanical properties of apples. Trying it might be the best approach. 
I notice that this site says a water pressure press gives 90% as much juice as a rack and cloth press. So water pressure may not be high enough to really do the job well. 
A: The key measure of how much juice is pressed out of the apples is the pressure in the apple container. It does not matter how this pressure is provided. Using the water press, as long as the rubber bladder is loose enough or flexible enough, the pressure which the apples are under is the same as the water pressure in the bladder.
The water pressure in the bladder depends on the height of the 'head' of water above the bladder. With the same 'head' of water, the apples will be under the same pressure whether the container is packed full of apples or packed loosely. The maximum 'head' which can be applied is limited by the strength of the rubber bladder and/or the apple container.
The economic advantage of packing apples tightly is that you should get more juice per pressing, because there are more apples in the press. The disadvantage with tight packing is that juice will have further to percolate through pulp to get to the outlet holes, so the amount of juice pressed from each kg of apples will be lower. The density of pulp will be the same in both cases, but the thickness will be greater. The same amount of juice will eventually percolate out of the apple pulp, but it will take much longer. 
So economically you are weighing the cost of having to re-fill the container more often when loosely packing apples, against the benefit of getting more juice per kg out of the apples. Depending on what the re-filling costs are, and the marginal profit per litre of juice, you could find a profit-maximising solution.
I agree with mmesser314 that this is really an engineering or economic question, Performing scaled experiments and calculating marginal profit would give you a more reliable answer than delving into the theoretical structural properties of apples and the diffusion of juice through pulp.
