Final answer:
Erythropoietin, produced by the kidneys, is the hormone that stimulates red blood cell production to increase oxygen delivery to tissues.
Step-by-step explanation:
The hormone that increases the production of red blood cells is erythropoietin. Erythropoietin is produced by the kidneys and is responsible for stimulating the production of red blood cells in the bone marrow. This hormone's release is triggered by low oxygen levels in the blood, ensuring that more oxygen can be delivered to tissues throughout the body by increasing the number of red blood cells. An excess of erythropoietin, especially when used artificially, can lead to increased blood viscosity and potential health risks.