Concept:
Pig iron is the raw, intermediate product of smelting iron ore with a high-carbon fuel and reductant. To produce it on an industrial scale, a specific type of continuous-operation furnace is required.
Step 1:
The primary raw materials used to produce pig iron are iron ore (like hematite or magnetite), coke (as fuel and reducing agent), and limestone (as a flux to remove impurities).
Step 2:
The reduction of iron ore requires an extremely tall, continuous counter-current reactor where hot gases rise and melt the descending raw materials at highly elevated temperatures (up to $2000^\circ$C).
Step 3:
A cupola furnace is primarily used in foundries for melting scrap iron or pig iron to cast into different shapes (cast iron), not for chemically reducing raw iron ore.
Step 4:
Electric arc furnaces and Open hearth furnaces are steelmaking furnaces. They are designed to refine existing pig iron and scrap steel by removing excess carbon to produce high-quality steel.
Step 5:
The Blast furnace is the massive, specialized industrial structure specifically built to smelt raw iron ore into liquid pig iron. Therefore, option (C) is the correct answer.