Final answer:
The implementation method that involves the most risk for a retail store chain developing a new integrated computer system for sales and inventories in its store locations is Direct cutover.
Step-by-step explanation:
The implementation method that involves the most risk for a retail store chain developing a new integrated computer system for sales and inventories in its store locations is Direct cutover. In a direct cutover, the old system is completely replaced with the new system in one go, which can be very risky as it may lead to system downtime and potential disruptions to store operations. This method requires careful planning and strong backup strategies to minimize the impact of any issues that may arise.