# Business Applications of Extrema

When we optimize business functions such as profit, revenue, or average cost, the functions are ultimately derived from financial data produced by the business. Ideally, these data would uniquely determine a function which could be optimized. However, conditions at a business normally do not allow the trends formed by cost and revenue data to be fit perfectly by a function. Costs vary due to fluctuations in the cost of materials, electricity, and labor. Prices may also change leading to fluctuations in revenue and profit. Functions like those in Section 12.3 are typically obtained through linear and nonlinear regression.

In this section, the objective functions we wish to minimize describe a particular variable cost and are constructed by examining the application. We’ll also look at designing an object with maximum volume subject to limitations on its dimensions. In each case, information about the application will be used to model the objective function. Once the objective function is in place, we’ll analyze the function to find its relative extrema using the derivative of the objective function.

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