A Firm Uses a Single Input to Produce Its Output

A firm uses a single input to produce its output, which is sold in a competitive market.It gets quantity discounts on purchases of its input.If it buys x units of the input, the price it must pay per unit of input is 289/x + 3.If it buys no inputs, it doesn't have to pay anything.The firm's production function is f(x) = 45x - x².If the price of the firm's output is 1, the profit-maximizing amount of input to buy is

A) 21.
B) 0.
C) 42.
D) 31.50.
E) None of the above.