Final answer:
According to the King and trustee's intentions, the British Empire expected to benefit from the establishment of a colony in Georgia by increasing its wealth through profitable production and trade, supported by an initial investment.
Step-by-step explanation:
The British Empire envisioned the colony of Georgia would benefit through increased wealth and by serving as a buffer zone. The initial investment by the parliament, based on James Oglethorpe’s influence and the Trustees' advocacy, aimed for Georgia to provide luxury items like wine and silk, although these plans did not come to fruition.
Instead, the colonists engaged in cattle farming, timber, and trade with Native Americans, which over time became primary sources of income and subsistence. The idea was that Britain would gain from these activities by receiving cheaper raw materials from Georgia and selling back manufactured goods at higher prices, thus establishing a favorable balance of trade and, ultimately, adding to the Empire's wealth as per mercantilism principles.