Final answer:
Josephine, as the executive vice president of sales and marketing, holds legitimate power due to her formal position in the organization, which is outlined by the authority inherent in her role and supported by the company's structure under rational-legal authority.
Step-by-step explanation:
Josephine, being the executive vice president in charge of sales and marketing, wields legitimate power in her role within the organization. This type of power is derived from her official position and the authority associated with it. Legitimate power is recognized by members of the organization and is conferred upon individuals by the formal roles and responsibilities they hold, as is the case with Josephine’s executive role.
Under the rational-legal authority as described by Max Weber, power is vested in the system or ideology and not solely in the person. An individual holding an official position such as Josephine's, within a rational-legal authority, is acknowledged as having the right to exercise power and make decisions pertaining to sales and marketing for the organization.
Accordingly, the presence of a structured hierarchy and formal job titles support the exercise of legitimate power. In the context of the options provided, 'legitimate' fits her power base most accurately, as it is tied to her formal authority as an executive within a company that operates under rational-legal authority.