a firm that produce car components has fixed costs of 40000 per month and variable cost of 24.00 per component, regardless of the number of units sold. find the break even point in units and explain it by means of a graph

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To find the break-even point in units, we need to determine the number of units of car components that need to be sold to cover the total costs.

The total costs for the firm consist of both fixed costs and variable costs. Fixed costs are constant and do not change with the number of units sold, while variable costs depend on the number of units produced and sold.

Given that the fixed costs are $40,000 per month and the variable cost per component is $24.00, we can calculate the total cost (TC) as follows:

TC = Fixed costs + (Variable cost per unit × Number of units)

To find the break-even point, we set the total cost equal to the total revenue (TR). At the break-even point, the total revenue earned from selling a certain number of units is equal to the total cost of producing those units.

Now, let's create a graph to visualize the break-even point. We will use the horizontal axis for the number of units sold (Quantity), and the vertical axis for the total cost and total revenue (in dollars). The intersection point on the graph represents the break-even point.

First, plot the fixed costs on the vertical axis. In this case, the fixed costs are $40,000, so draw a horizontal line at $40,000 on the graph.

Next, plot the variable costs as a function of quantity. Since each component has a variable cost of $24.00, draw a linear line that starts from the fixed costs line and has a slope of $24.00. This line demonstrates how the variable costs increase with the quantity of units produced.

Now, to plot the total costs, add the fixed costs line and the variable costs line. The total cost line will start at the fixed costs point and slope upwards, following the variable cost line. This line shows the total costs incurred for each level of quantity.

Finally, plot the total revenue line. The total revenue is calculated by multiplying the selling price per unit by the quantity sold. We do not have the selling price information in this question, so we cannot accurately depict the revenue line. However, for simplicity, let's assume that the selling price is equal to the variable cost per unit ($24.00). To plot the total revenue line, start at the origin (zero quantity) and draw a diagonal line with a slope equal to $24.00. Note that the total revenue line will always be above the total cost line since it represents the income from selling the units.

The break-even point occurs at the intersection of the total cost and total revenue lines on the graph. This is the point where the total revenue equals the total cost, indicating that the company is neither making a profit nor incurring a loss.

To identify the exact break-even point in units, locate the quantity value corresponding to the break-even point on the horizontal axis.

By analyzing the graph, you can easily visualize the break-even point and understand the relationship between costs and revenues at different levels of production.