Answer:
In a system of outcome-based ethics, the appropriate response would be to follow the customer's advice because what is paramount is the completion of the project. It is what is convenient for the business, the shareholders, and the project manager himself.
In a more morally-based ethical system, the appropriate system would be to either to refuse to inflate the costs, or to raise these costs only minimally. This in order to maintain financial similarity between reality and what was estimated. An ethical person also would opposed the furtherance of this practice of undervaluing costs in order to win licitations.