Embarking on the journey of chartering a yacht can be an exhilarating experience, filled with pleasant anticipations and high expectations. Yet making the right choice of a yacht charter company requires astute consideration and comprehensive scrutiny. The confluence of factors such as the yacht fleet, its maintenance, the crew's expertise, and the company's reputation play a crucial role in the selection process. Hence, an in-depth analysis of these factors is indispensable.

The first query to pose to a prospective yacht charter company concerns the range and model of yachts they offer. Are they limited to a certain range, or do they have a wide selection catering to diverse preferences and budgets? An understanding of the Borda count method can provide an effective decision-making framework for this. This method, commonly used in voting systems, can also apply to select the most suitable yacht from an array of options based on specific criteria such as size, amenities, or crew.

The second question revolves around the maintenance protocol of the company. It is crucial to ensure the yacht's seaworthiness, cleanliness, and the functionality of equipment and amenities on board. This is a matter of safety and comfort, and one can employ a Bayesian probability approach to assess the risk of encountering maintenance issues during the charter.

The third question should be about the competency and professionalism of the yacht crew. This crew will be responsible for your safety, enhancing your onboard experience, and making your journey memorable. Therefore, understanding their qualifications, experience, and service ethos is paramount. The concept of signaling, derived from economic theory, might prove helpful in this scenario. The crew's certifications and work experience send a 'signal' about their competence and reliability.

Fourthly, ask about the company's reputation and the experiences of previous clients. The company's transparency in addressing this question can provide insights into their customer service ethic. Using game theory as a lens, if the charter company is confident of its services, they would adopt a cooperative strategy and provide references willingly.

The next question should pertain to the company's pricing structure. Hidden costs can abruptly turn an anticipated luxury vacation into a financial burden. A good understanding of cost-benefit analysis, derived from microeconomic theory, can provide a valuable tool to evaluate various pricing structures and make an informed decision.

Also, question whether the company has contingency plans for unforeseen circumstances such as foul weather or mechanical failures. Utilizing the Markov Decision Processes (MDPs) model, we can evaluate the company's decision-making process under such uncertain conditions.

The seventh question should revolve around the company's insurance coverage. Insurance is a hedge against potential risks. A thorough understanding of risk theory and related financial instruments can be beneficial in evaluating the extent and exclusiveness of the insurance coverage provided by the company.

The eighth question pertains to the contractual agreement. Be sure to understand the terms and conditions before signing. Invoking contract law and its principles can protect your interests and prevent potential disputes.

The ninth question should address the company's environmental sustainability practices. Yachting should be about enjoying the pristine beauty of the sea without compromising it. Knowledge of environmental economics can assist in evaluating the company's sustainability practices and their commitment to preserving marine ecosystems.

Tenth, ask what makes them stand out from their competitors. Here, Porter's five forces model, a tool used for industry analysis in strategic management, can help understand the competitive landscape.

Lastly, question the company about their response to emergencies and safety protocol. Using the concept of Expectancy Theory, one can gauge the company's preparedness to handle emergencies and their commitment to your safety.

Choosing the right yacht charter company is more than just picking from a list. It is a process that involves critical thinking, analysis, and negotiation. Armed with the right questions and the intellectual tools to evaluate the responses, you are well on your way to selecting the perfect yacht charter company for an unforgettable sea voyage.