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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
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