In sub-parts (i) and (ii) choose the correct option and in sub-parts (iii) to (v), answer the questions as instructed.
A firm paid Rs. 25,000 as rent of its office and Rs. 15,200 as the interest of the loan taken to produce x units of a commodity. If the cost of production per unit is Rs. 8 and each item is sold at price of Rs. 75, find the break-even point.

Answer

To find the break-even point for the firm, we need to follow these steps:

### Step 1: Identify Fixed Costs
The fixed costs include the rent and the interest on the loan.

- Rent = Rs. 25,000
- Interest = Rs. 15,200

**Total Fixed Cost (FC)** = Rent + Interest
**Total Fixed Cost (FC)** = 25,000 + 15,200 = Rs. 40,200

### Step 2: Identify Variable Costs
The variable cost per unit of production is given as Rs. 8.

**Variable Cost (VC)** = Rs. 8 per unit
For x units, the total variable cost will be:
**Total Variable Cost (VC)** = 8x

### Step 3: Determine Revenue Function
The selling price per unit is Rs. 75. Therefore, the revenue function (R) for selling x units is:

**Revenue (R)** = Selling Price × Number of Units
**Revenue (R)** = 75x

### Step 4: Formulate the Cost Function
The total cost function (C) is the sum of fixed costs and variable costs:

**Cost Function (C)** = Total Fixed Cost + Total Variable Cost
**Cost Function (C)** = 40,200 + 8x

### Step 5: Formulate the Profit Function
Profit (P) is defined as Revenue minus Cost:

**Profit Function (P)** = Revenue - Cost
**Profit Function (P)** = R - C
**Profit Function (P)** = 75x - (40,200 + 8x)
**Profit Function (P)** = 75x - 40,200 - 8x
**Profit Function (P)** = 67x - 40,200

### Step 6: Find the Break-even Point
The break-even point occurs when profit is zero (P = 0):

67x - 40,200 = 0
67x = 40,200
x = 40,200 / 67
x = 600

### Conclusion
The break-even point is at **600 units**.

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