Explanation:

Break-even analysis is a financial tool used to determine the point at which a company's total revenue equals its total costs, resulting in neither profit nor loss. It helps businesses understand the number of units they need to sell to cover their costs and start making a profit. There are several assumptions made in break-even analysis, and the incorrect assumption is option 'C', which states that the selling price per unit varies with changes in production.

Assumptions of break-even analysis:

1. Variable costs remain constant per unit of output: This assumption implies that the cost of producing each unit of output remains the same regardless of the volume of production. In other words, the variable cost per unit does not change as the number of units produced increases or decreases. This assumption allows for easy calculation of the total variable cost by multiplying the variable cost per unit by the number of units produced.

2. Fixed costs remain constant at all volumes of output: This assumption assumes that fixed costs, such as rent, salaries, and utilities, do not change with changes in production volume. Fixed costs are those expenses that do not vary with the level of output or sales. By assuming that fixed costs remain constant, break-even analysis simplifies the calculation of the break-even point and provides a clear understanding of the minimum level of sales required to cover these fixed costs.

3. There is only one product or a constant sales mix: This assumption assumes that the company sells only one product or maintains a constant sales mix. It means that the proportion of each product sold remains constant regardless of the volume of production. This assumption is necessary to calculate the average selling price per unit accurately. If a company has multiple products with different selling prices, it becomes challenging to determine the average selling price per unit, which is crucial for break-even analysis.

4. Selling price per unit varies with changes in production: This is the incorrect assumption in break-even analysis. In reality, selling prices often change with changes in production volume. Factors such as economies of scale, demand and supply dynamics, competition, and market conditions can influence the selling price per unit. However, break-even analysis assumes a constant selling price per unit, which simplifies the calculation and provides a conservative estimate of the break-even point.

By not considering the variability in selling price per unit, break-even analysis may overestimate or underestimate the break-even point and the profitability of the business. Therefore, it is essential to consider market conditions and pricing strategies when applying break-even analysis in real-world scenarios.