Final answer:
Extended problem solving is most likely used for a silicon injection among the provided options, as it demands more consideration and assessment of risks than the other routine or low-cost alternatives.
Step-by-step explanation:
For the items listed, extended problem solving is most likely to be used for a decision involving a silicon injection. This is due to the nature of high involvement and potential risk associated with medical procedures requiring careful consideration and a substantial decision-making process.
In contrast, purchasing an ice cream cone, workout pants, or a bus ride typically involves routine problem solving or limited problem solving because they are more common, lower-cost, and involve less risk.