Final answer:
Andrew Carnegie stands out as a key figure who created new industries resulting in cheaper products, earning him the title 'Captain of Industry'.
Step-by-step explanation:
Captains of Industry and Andrew Carnegie
Among the men who created new industries resulting in cheaper products and earned the title Captains of Industry, Andrew Carnegie stands out. Carnegie revolutionized the steel industry by introducing methods that drastically reduced production costs and increased efficiency. Through his strategy of vertical integration, where he gained control over every aspect of steel production from raw materials to transportation and distribution, he ensured lower prices and better products in the steel market. His business practices and ability to produce more steel than all of Great Britain by the turn of the century affirm his status as a Captain of Industry.
On the other hand, Samuel Gompers, Eugene V. Debs, and Ida Tarbell had different roles during the era of industrialization. Gompers led labor unions, Debs was a union leader and socialist, and Tarbell was an investigative journalist who exposed corrupt business practices. They did not create industries themselves, thus referring to Carnegie is most accurate in the context of this question.