A company sells its product at the rate of Rs. 6 per unit. The variable costs are estimated to run 25% of the total revenue received. If the fixed costs for the product are Rs. 4500. Find the total cost function.

Answer

To find the total cost function for the company, we will follow these steps:

### Step 1: Define the Variables
Let:
- \( p \) = price per unit = Rs. 6
- \( F \) = fixed costs = Rs. 4500
- \( x \) = number of units sold

### Step 2: Calculate Total Revenue
Total Revenue (\( R \)) can be calculated using the formula:
\[ R = p \times x \]
Substituting the value of \( p \):
\[ R = 6x \]

### Step 3: Determine Variable Costs
The variable costs are estimated to be 25% of the total revenue. Therefore, we can express the variable costs (\( VC \)) as:
\[ VC = 0.25 \times R \]
Substituting the expression for \( R \):
\[ VC = 0.25 \times 6x = \frac{3}{2}x \]

### Step 4: Write the Total Cost Function
The total cost function (\( C(x) \)) is the sum of fixed costs and variable costs:
\[ C(x) = F + VC \]
Substituting the values of \( F \) and \( VC \):
\[ C(x) = 4500 + \frac{3}{2}x \]

### Final Answer
Thus, the total cost function is:
\[ C(x) = 4500 + \frac{3}{2}x \]

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