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$$\underset{K,L}{\text{max}}\;\;{F(K,L)−rK−wL}$$

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.

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    $\begingroup$ What do you mean by " increasing each factor of production by 1 when the existing number no longer supports"? $\endgroup$ – Brennan Sep 11 at 23:36
  • $\begingroup$ Imagine a factory, it has 2 workers, then the demand for the product that the factory has increases, the factory can make two decisions: continue with 2 workers and take more time to deliver, or increase by 1 the number of workers and continue to deliver on right time. In linear programming with the objective function being the minimization of costs(cost of each worker), and the restrictions being the demand, the company would also maximize the profit, did you understand? $\endgroup$ – KmnsE2 Sep 11 at 23:43
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    $\begingroup$ The cost minimization problem and the profit maximization problems are usually not duals of each other. $\endgroup$ – Tomcat Sep 12 at 5:55

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