Final answer:
When a firm doubles inputs and triples output, there are increasing returns to scale. To operate more efficiently in face of increased demand, a firm in the long run can acquire more capital and adjust its production function, allowing it to hire more workers efficiently.
Step-by-step explanation:
If a firm doubles inputs and produces three times the output, then there are increasing returns to scale. This means that the firm is operating more efficiently, getting more output per unit of input.
In the long run, to adapt to a situation where the firm's demand has increased to 15 documents per day and to maintain or improve efficiency, the firm could invest in more capital, such as acquiring two more PCs.
In this context the long run production function is relevant because it considers all factors as variable, which enables the firm to find the most efficient way of producing any given level of output, thus optimizing costs in the long run.