This mission pits you against four Pigs with the help of Richard the Lionheart on a map where economically you have very little. Zero access to farm land, difficulty seizing far away stone and iron, and with just a little bit of forest, you're basically on your own. With a mere 4000gp, how do you forge an economy from nothing? That's actually a thought construct I've been thinking about, and I have just the trick!
Our gamer challenge today is going to be defeating all of our enemies and protecting Richard with absolutely zero resources from our environment. We're going to buy in raw materials, sell finished products, and use the profit to build an army.
NOTE: This walkthrough is probably going to take longer than the opinion of others because we are going to specifically limit ourselves and not use woodcutters, quarries, or any other resource generation buildings. If you want something more straightforward or easy, you might want to go elsewhere.
Alright, so how do we build something from nothing (or rather, 4000gp)? Today we have two major champions: crossbows and bread. We also have three major benefactors: ale, bad things, and religion! Richard is going to chest-block the Pigs for us pretty well with his siege weapons, but he is going to need some help from us in order to stay standing. However, gladly we barely have to care about our defense because (in my playthrough) I was never attacked by the Pigs as long as Richard was alive.
We're going to start by wrapping our stockpile around our keep. On the left side we'll place our weapon sweatshop, on the right our baking sweatshop. North of the keep we'll place our supporting structures, and to the south our barracks and such.
Place a mill, brewery, and inn north of your keep (the inn can be father back, but you want the mill to have very close access to the stockpile). Place your marketplace wherever is convenient and and buy 5 wheat, hops, and ale for immediate inn functionality. Leaving only a one square gap, place a bakery along the eastern edge of the stockpile, and your granary behind it (with a single gap). On the other side of the keep, place a fletcher on with a single gap up against the stockpile, and the armory behind it with a single space gap. Then we'll place another bakery beside the first, and another fletcher beside the first. This is going to be the fledgling start to our economy. Some notes.
On the fletchers and bakeries, our eventual goal is to have sixteen of each surrounding it's storehouse of choice, built in pairs with single tiny gaps so workers can move and enter/exit well. Example like so, where s is the stockpile, x is the fletcher or bakery, and y is the armory or granary (Note the space between rows is just a single "pixel" not enough for a whole new building):
[x][x] [x][x] [x][x]
[x][x] [y][y] [x][x]
[x][x] [x][x] [x][x]
We want our granary set to ZERO rations (as long as we have one working alehouse per 30 citizens we won't need food), and we want all but one of our fletchers set to crossbows (the other I use to make archers to help defend Richard). Keep in mind that we will need to constantly be buying wheat, wood, and (far less so) hops to make this whole thing run, while selling every crossbow and loaf of bread we produce. At this point we want to place two more hovels as needed, so we have 26 citizens and we're running just under our 30 population cap for our first inn.
Now with the money we have left and our (presently) minor profit margins coming in, we have four ways we can spend our money to expand our business.  Building fletchers is costly and slow, but produces the best profit margins (3 wood costs 12gp to make a crossbow that sells for 30gp),  Building granaries has narrow profit margins but quicker production (one wheat costs 23gp, which turns into 1 flour which turns into 8 bread that sells for 32gp),  Bad Things are a costly investment that increase the profit margins of everything (especially your bread) but lower your combat strength (which we don't care about) and popularity. With the +8 ale counteracting your -8 food, you only have the +1 left from your taxes to use Bad Things unless you utilize  Religion. Paying 1000 gold for a cathedral gives you a constant +2 popularity, and a 500 church gives you a constant +1. If you then place a chapel or two next to your fletchers and bakeries you should have enough popularity left to even increase taxes.
Do it in whatever order you like, but the goal is 16 fletchers placed as above (15 on crossbows, one on longbows), 16 bakeries placed as above, two inns servicing no more than 60 people, and -5 Fear Factor for maximum productivity. Every time you sell bread, remember to buy back some wheat. Whenever you sell crossbows, buy some wood. Remember to buy hops every now and then and you are good. Starting out you might mess up and lose some time, but as long as you buy wheat and wood you'll be golden. Once you have a reserve of roughly 200 wood and 100 wheat you are ready to make your army.
This whole time I've been buying archers as my longbows come in and use them to guard Richard's mangonel. I gave the rest of my stone to Richard to help build him up, and threw him a 500gp care package as I could afford it so he could complete his walls and towers. By now perhaps two of the Pigs have some crossbows and and a tiny army, while the black and yellow Pigs, being hit by my archers and Richard's mangonel look ripe for the picking. With very few ranged units and a small wall to break through, time to use the cheapest siege force known to man; monks!
Monks are the second cheapest unit in the game at 10gp apiece. They are very slow and have no hit points, which means they get slaughtered by groups of ranged units. But they hit hard. Capable of tearing down castle walls nearly as well as macemen (and killing enemy lords too) and costing almost nothing, the monks are always my go-to unit when facing a lord that doesn't use a ton of archers.
For a mere 1000gp I built 100 monks, the cheapest siege force you'll ever find, and killed the yellow Pig, only losing 14. I noticed the black Pig (in between the other two) had incomplete walls and no units, so I killed him next. The other two had about 15 crossbowmen apiece as well as some macemen, but 150 monks each killed them without a problem.