If someone asks me to perform a task, as cheaply as possible, there’s no way for me to be cheap. It’s going to cost whatever I decide I want for the task. If however, they describe a desired outcome, I’m free to chose the cheapest task possible to get there.
Likewise if they want to maximize value, I can find the optimal task to do that too.
But I can’t find the cheapest way if I don’t have any options. The only way to have options is to understand what the final destination is.