Final answer:
Extended problem solving is used when consumers face significant investment decisions and perceive a high degree of purchase risk. Of the options provided, purchasing an audio system would most likely involve extended problem solving due to its complexity and cost.
Step-by-step explanation:
Extended problem solving is a consumer behavior where purchasers spend a lot of time searching for information and making comparisons before making a significant decision. This process is most commonly used in situations where the product has a high price, is not bought often, can be highly personal or represents a significant investment, and when the consumer perceives a high degree of purchase risk.
In the provided list, option c. audio systems most likely requires extended problem solving. Purchasing an audio system often involves comparison of features, quality, compatibility with other devices, brand reputation, and price. Due to the variety of options and the potential investment involved, consumers tend to engage in extended problem solving to ensure they make the right choice.