Final answer:
To complete this request, the administrator should use a Roll-Up summary to count the number of open cases associated with each account and update the account with this value every Friday evening.
Step-by-step explanation:
The administrator should use a Roll-Up summary to count the number of open cases associated with each account and update the account with this value every Friday evening. A Roll-Up summary is a feature in Salesforce that allows you to calculate and display the sum, minimum, maximum, or average of a field on all child records related to a parent record.
By creating a Roll-Up summary field on the Account object, the administrator can count the number of open cases related to each account. They can then schedule a weekly job to update the Roll-Up summary field with the count of open cases every Friday evening.
This approach is the most efficient and scalable way to handle the task at hand, as Roll-Up summaries are designed for this type of calculation and are optimized for performance.