With respect to the applications of dynamic optimisation, explain the optimal rate of extraction of exhaustible resources by monopoly. 

Dynamic optimization plays a crucial role in various fields, including economics, engineering, and environmental management. When considering the optimal rate of extraction of exhaustible resources under a monopoly, dynamic optimization principles are used to determine how a monopolistic firm should manage the extraction of a finite resource over time to maximize its long-term profits.

In the context of exhaustible resources, such as minerals, oil, or natural gas, the key challenge is to balance the current benefits of extraction with the potential costs of depleting the resource too quickly. Monopoly power adds an additional layer of complexity, as the monopolistic firm has the ability to influence both the quantity extracted and the price at which the resource is sold. This situation requires a dynamic optimization ___ ____ ___ ________ ___.
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