If the cost function of a certain commodity is `C(x)=2000+ 50x-(1)/(5)x^(2)` then the average cost of producing 5 units is

Options

A. Rs 451
B. Rs 450
C. Rs 449
D. Rs 2245

Answer

To find the average cost of producing 5 units of a commodity given the cost function \( C(x) = 2000 + 50x - \frac{1}{5}x^2 \), we will follow these steps:

### Step 1: Calculate the total cost for producing 5 units
We need to substitute \( x = 5 \) into the cost function \( C(x) \).

\[ C(5) = 2000 + 50(5) - \frac{1}{5}(5^2) \]

### Step 2: Simplify the expression
Now, we will simplify the expression step by step.

1. Calculate \( 50(5) \):
\[ 50(5) = 250 \]

2. Calculate \( \frac{1}{5}(5^2) \):
\[ 5^2 = 25 \quad \text{and} \quad \frac{1}{5}(25) = 5 \]

3. Substitute these values back into the equation:
\[ C(5) = 2000 + 250 - 5 \]

4. Combine the values:
\[ C(5) = 2000 + 250 - 5 = 2245 \]

### Step 3: Calculate the average cost
The average cost \( AC \) is calculated by dividing the total cost by the number of units produced.

\[ AC = \frac{C(5)}{5} = \frac{2245}{5} \]

### Step 4: Perform the division
Now we will perform the division:

\[ AC = \frac{2245}{5} = 449 \]

### Conclusion
The average cost of producing 5 units is \( \text{Rs. } 449 \).