Final answer:
Muscles require the least blood supply when the body is at rest. They experience vasoconstriction, reducing blood flow until there is a higher demand during exercise or other activities.
Step-by-step explanation:
The organs that require only a minimal blood supply when at rest are the muscles. During periods of rest, the blood flow to skeletal muscles is reduced due to vasoconstriction, meaning the contraction of the blood vessel walls. On the other hand, during exercise, there's an increased demand for oxygen and nutrients, leading to vasodilation, the widening of blood vessels, to allow more blood flow to these active tissues. The heart, lungs, and other vital organs have more consistent blood supply demands to maintain their high-functioning roles regardless of a person’s physical activity level.
Regarding the options provided in the question, the kidneys experience vasoconstriction, reducing blood supply when not as active. The urinary system relies on the kidneys for filtration and blood regulation, but since this process can be highly variable, it's adjusted based on the body’s needs and the state of hydration. Hence, muscles (C) are the correct answer because they are the tissues that will experience the most drastic decrease in blood supply when the body is at rest.