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Variable costs are expenses that change in proportion to the activity of a business. In other words, they are costs that vary depending on the level of production or sales volume. For example, the cost of direct materials is a typical variable cost. As production increases, more materials are required, thus increasing the total cost. Conversely, when production decreases, the material costs fall accordingly.

In the Applewhite Corporation scenario, the cost of direct materials for products would indeed be classified as a variable cost (Statement I). This is because with every additional unit produced, the company would need additional materials, hence incurring extra material costs. When it comes to learning about cost accounting, it is essential to understand the nature of variable costs and how they contribute to the overall cost of production.

Fixed costs, on the other hand, do not vary with the level of production or sales volume. They are expenses that remain constant, regardless of how much a company produces or sells. Common examples of fixed costs include rent, salaries, and depreciation of assets.

Depreciation of plant machinery, as mentioned in Statement II regarding Applewhite Corporation's costs, is typically a fixed cost. Even though the company uses an accelerated depreciation method, which is a way of calculating depreciation more quickly during the initial years of an asset's life, the depreciation expense itself does not increase or decrease with the production level. It is a cost that the business will incur regardless of its manufacturing activity. Understanding the distinction between fixed and variable costs is crucial in cost behavior analysis and management decision-making processes.

Cost behavior analysis is the study of how different costs change with changes in the level of business activity. It involves understanding and categorizing costs as either fixed, variable, or mixed (having both fixed and variable components), to make informed business decisions about budgeting, pricing, and managing expenses.

Electricity costs, as given in Statement III, typically exhibit a mixed cost behavior. A portion of the electricity cost remains constant regardless of the factory's output (fixed component), while another portion fluctuates with the level of production (variable component). When performing cost analysis, it's important not to oversimplify by labeling a mixed cost as purely fixed or variable. Instead, cost behavior analysis would require dissecting the electricity bill to determine the fixed base charge and the variable rate per unit of electricity consumed. Accurate cost behavior analysis assists a company like Applewhite Corporation in controlling costs effectively and making strategic operational decisions.