A firm produces 50 units of a good for Rs. 320 and 80 units for Rs. 380 . Supposing that the cost curve is a straight line, estimate the cost of producing 110 units :

Options

A. Rs. 330
B. Rs. 1665
C. Rs. 440
D. Rs. 365

Answer

To solve the problem step by step, we will use the information given about the production costs at two different levels of output.

### Step 1: Identify the points
We have two points based on the information provided:
- Point A (50 units, Rs. 320) → (x1, y1) = (50, 320)
- Point B (80 units, Rs. 380) → (x2, y2) = (80, 380)

### Step 2: Calculate the slope (m)
The slope of the line (m) can be calculated using the formula:
\[ m = \frac{y2 - y1}{x2 - x1} \]

Substituting the values:
\[ m = \frac{380 - 320}{80 - 50} = \frac{60}{30} = 2 \]

### Step 3: Write the equation of the line
The equation of a straight line can be expressed in the form:
\[ y = mx + c \]
Where:
- m is the slope we just calculated (m = 2)
- c is the y-intercept, which we need to find.

So, we have:
\[ y = 2x + c \]

### Step 4: Find the y-intercept (c)
To find c, we can use one of the points. Let's use Point A (50, 320):
\[ 320 = 2(50) + c \]
\[ 320 = 100 + c \]
\[ c = 320 - 100 = 220 \]

### Step 5: Substitute c back into the equation
Now substituting c into the equation:
\[ y = 2x + 220 \]

### Step 6: Calculate the cost for 110 units
Now, we need to find the cost when x = 110:
\[ y = 2(110) + 220 \]
\[ y = 220 + 220 \]
\[ y = 440 \]

### Conclusion
The estimated cost of producing 110 units is Rs. 440.