Final answer:
The hormone oxytocin is produced in the hypothalamus, along with vasopressin or ADH, while the anterior pituitary gland produces hormones like GH, prolactin, and TSH.
Step-by-step explanation:
The hormone oxytocin is produced in the hypothalamus. It is one of two hormones (the other being vasopressin or Anti-diuretic Hormone, ADH) that are synthesized by the neurons of the hypothalamus. While the anterior pituitary gland is responsible for the production of several hormones such as growth hormone (GH), prolactin, and thyroid-stimulating hormone (TSH), the hypothalamus produces hormone-releasing factors like thyrotropin-releasing hormone (TRH) that regulate the secretion of pituitary hormones.