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The answer is: you should use the methods in which you ask people to name their price. The idea behind this answer is quite simple. By asking people to name their price you're basically making them reveal which is the shape of the demand curve. That is, you know whether there are a large number, a medium number, or a small number of fans. Since the optimal selling price is different for each type of demand, you're able to choose this optimal price once you know the demand type. Let's see this in more detail.
If you choose the first alternative (you choose the price first), you have:
Price Expected sales Exp. Profit
8 0.2*15 + 0.3*12 + 0.5*9 = 11.1 ...
The solution answers the question(s) below.