Final answer:
The designated manager for narcotics cannot be a non-pharmacist manager in a community pharmacy due to the strict regulations requiring a licensed professional like a pharmacist with a background in chemistry and biology.
Step-by-step explanation:
The task that cannot be delegated to a non-pharmacist manager of a community pharmacy is d. being the designated manager for narcotics. This is because the management of narcotics is strictly regulated and requires a professional who is licensed and has the expertise to handle controlled substances, which in a pharmacy setting would be the pharmacist. Pharmacists are trained and equipped with knowledge in chemistry and biology to understand the medical implications and legal responsibilities associated with dispensing narcotics. Other tasks such as direct order purchasing, contracting for computer systems, and supervising staff time sheets can generally be performed by non-pharmacist managers as they do not require the same level of pharmaceutical knowledge or legal responsibility.