If the relationship between total cost and number of units made is linear, and if cost increased by
$3 for each additional unit made, and if the total cost of 10 units is $30, find the equation of the
relationship between total cost (y) and number of units made (x)
Answers
Answer:
Perimeter of rectangle = 2 (Length + Breadth)
= 2 (x + y)
= 2 x + 2 y
Step-by-step explanation:
Perimeter of rectangle = 2 (Length + Breadth)
= 2 (x + y)
= 2 x + 2 y
Answer:
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Step-by-step explanation:
Variable costs are expenses that vary in proportion to the volume of goods or services that a business produces. In other words, they are costs that vary depending on the volume of activity. The costs increase as the volume of activities increases and decrease as the volume of activities decreases.
The Most Common Variable Costs
Direct materials
Direct labor
Transaction fees
Commissions
Utility costs
Billable labor
Essentially, if a cost varies depending on the volume of activity, it is a variable cost.
Formula for Variable Costs
Total Variable Cost = Total Quantity of Output x Variable Cost Per Unit of Output
Variable vs Fixed Costs in Decision-Making
Costs incurred by businesses consist of fixed and variable costs. As mentioned above, variable expenses do not remain constant when production levels change. On the other hand, fixed costs are costs that remain constant regardless of production levels (such as office rent). Understanding which costs are variable and which costs are fixed are important to business decision-making.
For example, Amy is quite concerned about her bakery as the revenue generated from sales are below the total costs of running the bakery. Amy asks for your opinion on whether she should close down the business or not. Additionally, she’s already committed to paying for one year of rent, electricity, and employee salaries.
Therefore, even if the business were to shut down, Amy would still incur these costs until the year-end. In January, the business reported revenues of $3,000 but incurred total costs of $4,000, for a net loss of $1,000. Amy estimates that February should experience revenues similar to that of January. Amy’s list of costs for the bakery is as follows:
A. January fixed costs:
Rent: $1,000
Electricity: $200
Employee salaries: $500
Total January fixed costs: $1,700
B. January variable expenses:
Cost of flour, butter, sugar, and milk: $1,800
Total cost of labor: $500
Total January variable costs: $2,300
If Amy did not know which costs were variable or fixed, it would be harder to make an appropriate decision. In this case, we can see that total fixed costs are $1,700 and total variable expenses are $2,300.
If Amy were to shut down the business, Amy must still pay monthly fixed costs of $1,700. If Amy were to continue operating despite losing money, she would only lose $1,000 per month ($3,000 in revenue – $4,000 in total costs). Therefore, Amy would actually lose more money ($1,700 per month) if she were to discontinue the business altogether.
This example illustrates the role that costs play in decision-making. In this case, the optimal decision would be for Amy to continue in business while looking for ways to reduce the variable expenses incurred from production (e.g., see if she can secure raw materials at a lower price).
Example of Variable Costs
Let us consider a bakery that produces cakes. It costs $5 in raw materials and $20 in direct labor to bake one cake. In addition, there are fixed costs of $500 (the equipment used). To illustrate the concept, see the table below:
Variable Costs Example Calculation
Note how the costs change as more cakes are produced.
Break-even Analysis
Variable costs play an integral role in break-even analysis. Break-even analysis is used to determine the amount of revenue or the required units to sell to cover total costs. The break-even formula is given as follows:
Break-even Point in Units = Fixed Costs / (Sales Price per Unit – Variable Cost per Unit)
Consider the following example:
Amy wants you to determine the minimum units of goods that she needs to sell in order to reach break-even each month. The bakery only sells one item: cakes. The fixed costs of running the bakery are $1,700 a month and the variable costs of producing a cake are $5 in raw materials and $20 of direct labor. Additionally, Amy sells the cakes at a sales price of $30.
To determine the break-even point in units:
Break-even Point in Units = $1,700 / ($30 – $25) = 340 units
Therefore, for Amy to break even, she would need to sell at least 340 cakes a month.
Video Explanation of Costs
Watch this short video to quickly understand the main concepts covered in this guide, including what variable costs are, the common types of variable costs, the formula, and break-even analysis.
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