Final answer:
Melatonin is the hormone produced by the pineal gland that induces sleepiness, and its production is increased in darkness and decreased in light, managing the sleep-wake cycle.
Step-by-step explanation:
The hormone manufactured by the pineal gland responsible for making one feel sleepy is melatonin. This gland, located in the brain, signals the body to prepare for sleep in response to darkness. The secretion of melatonin increases as light levels decrease, facilitating the sleep-wake cycle. In contrast, exposure to light inhibits this production, promoting wakefulness. Therefore, melatonin plays a critical role in maintaining circadian rhythms.