# (Monopoly.) The hatters of Wo

**Question description**

(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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