$$\underset{K,L}{\text{max}}\;\;{F(K,L)−rK−wL}$$
What is the difference between maximizing profit using this process above, or simply increasing each factor of production by 1 when the existing number no longer supports? Is there a big difference in these two forms?
the above method can be solved using lagrange method, but isn't it much simpler to create a linear programming model with the capacity constraints of each production factor?
it seems to me that the classic way that microeconomics shows how the company maximizes profit is something much more theoretical than practical.