Final answer:
According to the corporate opportunity rule, Alan can only pursue the business opportunity after offering it to DollarShopper Corp., and if they reject it.
Step-by-step explanation:
Under the corporate opportunity rule, Alan, as a corporate manager at DollarShopper Corp., must adhere to certain fiduciary duties. One of these duties is the duty of loyalty, which prohibits Alan from exploiting a business opportunity that should belong to the corporation without first offering it to DollarShopper. The correct course of action Alan should take, according to this rule, is option 3: pursue the business opportunity only if he first offers it to DollarShopper, and the corporation rejects it. This ensures that the corporation's interests are not compromised by the personal interests of its managers.