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In this scenario, we use calculus to determine the optimal operating specifications of a chemical extraction process. The results are achieved by first developing an expression that yields the total annual cost of the process. Factoring in electricity, vessel, agitator, and solvent costs, an annual cost expression was fabricated. AGIEX company manufactures a certain amount of a product, A, which has an impurity that it wishes be reduced. By engineering an optimally sized vessel to perform the extraction of impurity, the company will save costs by ensuring no inefficient spending on power or excess solvent occurs. A specific amount of electricity is required to operate this vessel during extraction batches. These values of optimal vessel volume and power usage per batch ultimately form the boundaries of this streamlined system for the company.

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Brian Curtin, Mathematics and Statistics

Scott Campbell, Chemical and Biomedical Engineering

Problem Suggester:

Scott Campbell