Okay, so I've been asked to draw out my example for an additional 10 turns. This, of course, assumes you've not yet grown to your happiness cap. For the sake of argument, we'll assume a happiness cap of 7. If you'd like to make this 8 or 9, then we could, but it would change the way both cases are managed (without substantially changing the conclusions that could be drawn).
Before I jump into the specific examples and the overly complicated charts, I'd like to repeat the principle that ensures that, in low(ish) pop scenarios with a food surplus that outstrips the available hills, slavery is better able to convert excess food into hammers. If you'd like that excess food to go into growth instead, that's fine, but in either case you'll be sacrificing some degree of hammer output in order to acheive that growth. For whipping, you'd whip less often; for non-whipping, you'd spend time working farms instead of mines.
So, the whipped case...
This was very straight-forward. The only real rule behind it was to always work the highest food tiles available. Since those are often grassland-cottages, so much the better. It's running at a 5-food surplus the entire time. This comes from the center tile (+2), a floodplain cottage (+1), and a 4-food tile (+2, unirrigated rice).
Code:
Turn FoodBar Pop Food Hammers Cottages
0 16/26 3 5 90 2
1 21/26 3 5 0 2
2 13/28 4 5 0 3
3 18/28 4 5 0 3
4 23/28 4 5 0 3
5 14/30 5 5 0 4
6 19/30 5 5 0 4
7 24/30 5 5 0 4
8 29/30 5 5 0 4
9 19/32 6 5 0 5
10 24/26 3 5 90 2
11 16/28 4 5 0 3
12 21/28 4 5 0 3
13 26/28 4 5 0 3
14 17/30 5 5 0 4
15 22/30 5 5 0 4
16 27/30 5 5 0 4
17 17/32 6 5 0 5
18 22/32 6 5 0 5
19 27/32 6 5 0 6
20 16/34 7 - - -
SUM 180 73
So, in order to get an output of 180 hammers, 73 turns could be spent working cottages. Not too shabby.
Now, the non-whipped case.
This is a little more complicated from a tile management perspective. I had to throw in a plains hill in order for the simultaneous goals of growth and an equivalent hammer output to be realized. Note that this is now requiring 4 hills, a plot that would oft-times be better suited for a production city. Specifically, we now have enough hills to fully consume our food surplus, that is one of the distinguishing characteristics of a production city. I'll just throw the chart up first and explain the tile usage afterwards.
Code:
Turn FoodBar Pop Food Hammers Cottages
0 16/32 6 5 0 5
1 21/32 6 5 0 5
2 26/32 6 5 0 5
3 31/32 6 1 10 2
4 16/34 7 0 13 2
5 16/34 7 0 13 2
6 16/34 7 0 13 2
7 16/34 7 0 13 2
8 16/34 7 0 13 2
9 16/34 7 0 13 2
10 16/34 7 0 9 4
11 16/34 7 0 9 4
12 16/34 7 0 9 4
13 16/34 7 0 9 4
14 16/34 7 0 9 4
15 16/34 7 0 9 4
16 16/34 7 0 9 4
17 16/34 7 0 9 4
18 16/34 7 0 9 4
19 16/34 7 0 9 4
20 - -
SUM 178 69
There are 3 distinct phases in the tile utilization patterns above. To start out, they're trying to grow as quickly as possible, working all available food tiles and cottages (similar to the whipped case). One turn is spent transitioning to the next phase. During this transition, I'm working the floodplain, 2 grass-mines, 1 plains-mine, the 4-food tile, and a cottage. This give a surplus food of 1 and ensures that the two examples end at the same point in the food bar. After securing the growth to 7, the city begins spitting out as many hammers as possible, working all available mines and food tiles (3 grass-mines, 1 plains-mine, 1 floodplain, 1 4-food, 1 cottage). During the last phase, we've laid off the mines a bit (no longer working the plains-mine) in order to spend time working more cottages.
After all was said and done, the whipped case had higher output in both hammers and commerce (and received those hammers sooner).