How do I increase the number of workers in an industrial area?
"Given that I am still at level 1 and only have one of each type of building, does it mean I have to build multiple plantations and sawmills?"
Correct. Also ensure that:
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Your city has industrial demand, so that workers will actually fill up open industry jobs.
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Road connections to your industry buildings are not blocked by traffic, destroyed, flooded etc.
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Industry buildings are not operating at reduced capacity. All utilities (electric, water, sewage) should be provided.