For businesses, saving even a small amount of money can make a big difference over the course of days, months and years. Leaders have a variety of formulas they use to come up with that cost savings, which means first studying exactly what they’re currently spending and finding a way to cut back. One way to determine how much your own company is spending is to calculate the total cost to produce a set number of items. This will help you predict how that will change over time, known as the cost function.

#### TL;DR (Too Long; Didn't Read)

In business, the cost function formula is your fixed costs plus your variable costs, which combine to form your total production cost.

## Cost Function Formula

Every business has costs, some of which are variable and some of which are fixed. For a company, monitoring those costs can be important, since cutting back on those costs can save money. If a business can find a way to keep expenses down, that means being able to reduce its cost per item, thereby increasing profits. Unfortunately, costs don’t remain stagnant. Everything from the price of parts to the monthly electricity bill can fluctuate from one month to the next, making it difficult to track exactly how much is being spent.

To determine the combination of variable and fixed costs, businesses use a cost function calculator, which captures expense fluctuations by using a formula. Leaders track information on costs and input them into an equation, which then gives the total production cost. As expenses vary from one month to the next, managers can monitor that cost and make adjustments as needed.

## Fixed Costs vs. Variable Costs

Before you can put your cost function formula to use, it can be helpful to first understand the difference between fixed and variable costs. A fixed cost is something that doesn’t change from one month to the next. In manufacturing, fixed costs might be rent, salaries or property taxes. Although these items can be reevaluated on a periodic basis and adjusted, you can count on them generally remaining the same as you set next month’s budget. If any expense passes that test, it’s a fixed expense.

Variable expenses, on the other hand, are far less predictable. Often, variable costs happen because your order volume has gone down. Maybe you were outputting 100,000 widgets last month and your orders dropped to 80,000 this month, which means you’ll use fewer materials and electricity. You may also be able to scale back on labor and production costs depending on whether you’re set up to use fewer machines and workers when demand drops. The more fixed costs you have, the more money you’ll lose if your orders decline. The good news is that if orders increase, those fixed costs won’t go up unless you have to scale upward to maintain the same production levels, such as adding additional shifts or purchasing more equipment, for instance.

## How to Find Cost Function

The cost function equation is C(x)= FC(x) + V(x). In this equation, C is total production cost, FC stands for fixed costs and V covers variable costs. So, fixed costs plus variable costs give you your total production cost. Once you’ve determined your total production cost, you’ll be able to better budget your expenses since you’ll know exactly what you spent each month, all factors considered. Even with costs varying, you may be able to look at your production cost from one month to the next and note that, for example, in January your orders drop each year and therefore your total production cost will go down as a result.

If you’re solving for cost function, you usually want to determine exactly how much it will cost to manufacture a specific number of items within a certain time frame. So, if you anticipate an order of 100 widgets per month initially, to determine exactly how much you’ll spend to make that happen you’ll add up all fixed and variable costs, arriving at your total production cost. You can then determine how much you’ll need to charge to either make a profit or break even, depending on your company’s goals.

## How to Find Profit Function

Another important part of the cost function equation is the profit function. This equation helps you determine exactly how much profit you are making on the products or services. In basic economics, you’re taught to use this to determine exactly how much you should charge. The profit function is P(x) = R(x) - C(x), with P representing profit, R standing for revenue and C being cost. So, you’re subtracting your cost from your revenue to determine how much profit you’re making.

Like the cost function calculation, though, you’ll need to gather information before you can work the equation. This means knowing exactly what your revenue was for the time period as well as your fixed and variable costs. You should be monitoring this information already. If you regularly watch your business’s profit function, you’ll be able to determine exactly how profitable you are.

## How to Find Revenue Function

If you’re going to apply a profit function or cost function equation to your processes, it can also help to fully understand your revenue. In fact, you’ll need to know this calculation before you can determine your profit function. Your revenue is an important figure because it tells you exactly how your business is performing. If revenue goes down, it’s a problem that needs to be solved. The sooner you can start watching your monthly revenue, the more quickly you’re likely to catch a drop in revenue so that you can fix it. When you combine it with your cost function, you’ll even be able to look at areas where you can cut back on expenses to make up for falling revenue.

Determining revenue is fairly straightforward. The revenue function is R(x) = U(x) * P(x), where R is sales revenue, U is units sold and P is sales price. So, you would be multiplying units sold by price to determine your total sales revenue. You’ll want to measure this number against figures from other time periods to determine how your business is performing. You may want to compare this month’s figures to last month, the entire year or the same month last year.

## Cost Function for Services

If you run a service-based business, you may wonder how the cost function formula can apply to you. You don’t sell products, after all, so how can you determine how much it costs to make what you’re offering? The cost function equation can apply to a service-based business. You’ll still have fixed and variable costs to operate each month, no matter what type of business you run. Instead of producing and selling widgets, though, you’re interacting with clients and collecting money for services rendered.

To run the cost function calculator on your service-based business, you’ll simply need to determine the fixed and variable costs you have each month to arrive at your total production cost. In this case, the cost relates to what you spend to provide those services each month, including salaries, equipment, transportation and marketing. You’ll also have the standard operating costs such as rent and utilities. Calculating your profitability means taking all of those expenses and subtracting them from the money you’re bringing in each month. As with product-based businesses, monitoring your monthly and yearly revenue can help you immediately identify when you have a drop that needs to be addressed.