(Monopoly.) The hatters of Wo

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 (Monopoly.) The hatters of Wonderland make top hats from cardboard. They are wasteful when hurried so their production function is x = √ r where x is the number of hats made and r is the number of sheets of cardboard used. (For example, 1 hat requires 1 sheet, but 2 hats requires 4 sheets because of wasted material.) Alice is a monopolist in the hat business, with many hatter employees. Cardboard costs her $1 per sheet. (a) Find the cost of production C(x). (b) The demand for cardboard hats follows the price-demand equation px = 30 Find the number of hats Alice should produce to maximize her profit. (Important hint: what is the domain of the function?)

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