but how do I defeat them when I start with 50 gold, and the farmers produce gold at such a slow rate
A good strategy I use is filling the 3rd column with farmers, and dropping mines when enemies spawn. With a column full, then I start placing archers and arbalists on the 1st & 2nd columns behind the farmers and fill the 4th column with more farmers. When the witches throw their charm spells, let it hit the farmer, remove them off the field, and replace them immediately.