The aim of the question is to find the **two assumptions** which are considered while estimating the **cost function.**

The basic concept behind estimating cost function is **cost behavior analysis**. Cost behavior analysis identifies the change in the **total cost** of the product at the end due to the change in its **activity level.** For this purpose **mathematical cost functions** are used.

There are two types of costs:

**Variable cost****Fixed cost**

Here, **Fixed cost remains fixed** throughout until the end, whereas the variable cost, as the name suggests, **varies** with change in the activity level.

## Expert Answer

**Cost functions** can be represented in the form of an **equation** or **graphical representation** for a better understanding. Its representation in the form of an equation includes the variables on which cost function depends, a slight change in these variables thus has a significant effect on the total cost.

We know that the equation for **cost function** is:

\[ cost model = fixed cost + variable cost \times x \]

It can also be represented as:

\[ y = ax + h \]

where,

**$y=$ value at $y-axis$**

**$a=$ numerical value with axis $x$**

**$x =$ value at $x-axis$**

**$h=$ numerical value**

To represent a cost function following **two points** are kept in mind:

- Changes in the
**cost function**variables depict the change in the final cost. - The cost function is considered a
**linear function.**

There are different methods for **Cost Analysis**, which include,

** -Quantitative Analysis**

** -High-Low Cost Analysis**

** -Regression Cost Analysis**

In **quantitative analysis**, the easiest method is the high low-cost method. In the **high low-cost method**, we consider the highest and the lowest costs in the data set to determine the total cost function.

In the **Regression Analysis**, we not only consider the highest and the lowest values but the rest of the variables as well, and with the help of software such as **Microsoft excel** we get the required cost function. This method is more accurate and the probability of error is also less.

## Numerical Results

To represent a cost function following two basic points are considered:

- Changes in the
**cost function**variables depict the change in the final cost. - The cost function is considered a
**linear function**.

## Example

A **Petroleum industry** manager wants to find out the **cost analysis equation** for the given data set below by applying **high-low** cost behavior. Find out the full **cost function.**

**Days Total overhead cost Labor hours**

Monday $10,000 100

Tuesday $5,000 50

Wednesday $1500 18

Thursday $8000 75

Friday $11,000 135

Saturday $2000 24

Sunday $9000 98

So we gather information for highest and lowest observation:

**Highest value = $11,000 **

**Highest unit = 135**

**Lowest value = $1500 **

**Lowest unit = 18**

**Difference value = $9500**

**Difference unit = 117**

\[Slope = \frac {9500}{117} =81.20 \]

**Variable cost per unit = $81.20**

**fixed cost = $38.46**

Equation for **cost function** is:

\[ cost\ model = fixed\ cost + variable\ cost\times x \]

\[ cost\ model = 38.46 + 81.20 \times x \]