Answer :
Final answer:
Using the Lagrange Multipliers method, the estimated cost for a production increase from 56 to 57 would be approximately 1320.
Explanation:
The problem refers to economic optimization and uses a method from calculus known as the Lagrange Multipliers, expressed as λ in the problem. From the information given, the current production corresponds to f(49,83)=1300. The coefficient λ=20 relates to how sensitive the cost is to changes in the production quantity.
The question asks us to estimate the cost if the production quota is raised to 57. Since the change in production is small (from 56 to 57), we can use the principle of marginal cost, which in this case is represented by λ. The change in cost will be approximately λ * change in quantity, resulting in an increase of (57-56) * 20 = 20. So, the estimated cost when the production is raised to 57 would be original cost plus the increase, resulting in 1300 + 20 = 1320.
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