The marginal cost of a product is given by MC = 2x + 30 and the fixed cost is Rs. 120. Find
(i) the total cost of producing 100 units.
(ii) the cost of increasing output from 100 to 200 units.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
- The marginal cost (MC) is given by the equation:
\[ MC = 2x + 30 \]
- The fixed cost (FC) is given as:
\[ FC = 120 \]

### Step 2: Find the total cost function
The total cost (TC) can be found by integrating the marginal cost function with respect to \(x\):

\[ TC = \int MC \, dx = \int (2x + 30) \, dx \]

### Step 3: Perform the integration
Integrating \(2x + 30\):

\[ TC = \int (2x + 30) \, dx = x^2 + 30x + C \]

Where \(C\) is the constant of integration.

### Step 4: Determine the constant \(C\)
To find \(C\), we use the fact that when \(x = 0\) (no units produced), the total cost is equal to the fixed cost:

\[ TC(0) = FC = 120 \]

Substituting \(x = 0\) into the total cost equation:

\[ TC(0) = 0^2 + 30(0) + C = C = 120 \]

Thus, the total cost function becomes:

\[ TC = x^2 + 30x + 120 \]

### Step 5: Calculate the total cost of producing 100 units
Now, we can find the total cost when \(x = 100\):

\[ TC(100) = 100^2 + 30(100) + 120 \]

Calculating this:

\[ TC(100) = 10000 + 3000 + 120 = 13120 \]

### Step 6: Calculate the total cost of producing 200 units
Next, we find the total cost when \(x = 200\):

\[ TC(200) = 200^2 + 30(200) + 120 \]

Calculating this:

\[ TC(200) = 40000 + 6000 + 120 = 46120 \]

### Step 7: Calculate the cost of increasing output from 100 to 200 units
The cost of increasing output from 100 to 200 units is given by:

\[ \text{Cost increase} = TC(200) - TC(100) \]

Substituting the values we calculated:

\[ \text{Cost increase} = 46120 - 13120 = 33000 \]

### Final Answers
(i) The total cost of producing 100 units is **Rs. 13120**.
(ii) The cost of increasing output from 100 to 200 units is **Rs. 33000**.