Owner's Plan:
1. Identify the team with the highest average projected completion time.
2. Retrain that team to improve its efficiency.

Goal: Improve worker efficiency and reduce costs.
We are looking for an option that most seriously calls into question this plan for selecting the team to be retrained. This means the option should suggest that selecting the team solely based on "highest average projected completion time" might be flawed or unfair, and thus the retraining might not target the true inefficiency.

Let's evaluate each option:
- A. The installation fees that the firm charges its customers are lower than those charged for similar projects done by other companies.
- This provides information about pricing strategy, not directly about worker efficiency or the effectiveness of the retraining plan. It doesn't question how the team is selected for retraining.
- B. If the time that the team takes to finish a project is not lowered significantly, the firm could lose business to competitors.
- This emphasizes the importance of reducing completion time, but it doesn't question the method of selecting which team to retrain. It supports the goal of the retraining, not critiques the selection process.
- C. The team that has the highest average completion time tends to be assigned the most complex projects.
- This is the strongest challenger to the plan. If the team with the highest average completion time is consistently assigned the most complex projects, then their longer times might not be due to inefficiency but rather to the inherent difficulty and time requirements of the tasks they handle.
- Retraining them based solely on average time would be unfair and might not address true inefficiency if other teams are working on simpler projects that naturally take less time. The owner's metric (average completion time) would be flawed if it doesn't account for project complexity.
- D. Retraining the team will substantially increase the short-term costs of the firm and thereby impact its profitability.
- This points out a downside of retraining (increased costs), but it doesn't question the logic of selecting that particular team for retraining. It questions the impact of the retraining, not the selection method.
- E. Maximum efficiency can only be achieved if the team with the highest average completion rate is terminated.
- This offers an alternative, more drastic solution (termination) and suggests a different path to "maximum efficiency," but it doesn't directly question the owner's plan for selecting the team to be retrained (i.e., whether average completion time is the right metric). It offers a different action rather than a critique of the selection criterion.

Conclusion:

Option (C) directly attacks the premise of the owner's selection method. If average completion time is inflated by project complexity, then using that metric alone to identify inefficiency is flawed.

The final answer is C .