How Demand For Any Factor Of Production Affects The Profit Maximizing Firm?

Imagine that you are a profit-maximizing farmer. In your area, you can hire all the farmhands you want at $20,000 per year. Your accountant hands you a spreadsheet with the data. How would you proceed?
You could try different possibilities. If you hire one worker, the additional revenue is $60,000 while the marginal cost of the worker is $20,000, so your extra profit is $40,000. A second worker gives you and revenue of $30,000 for an additional profit of $10,000. The third worker produces extra output yielding revenue of only $15,000 but costs $20,000, hence it is not profitable to hire the third worker. The maximum profit is earned by hiring two workers. We have by trial and error found an interesting rule:
A firm will maximize profits by hiring a factor of production as long as the revenue of that input exceeds the extra cost of that input.
By using this reasoning, we can derive the rule for choosing the optimal combination of inputs: to maximize profits, inputs should be added as long as the marginal revenue product of the input exceeds the marginal cost or price of the input.