The correct option is: B
The cost function as C(x), where x is the number of units produced. We know that the cost for 250 units is Rs. 4000, so we can write the equation:
C(250) = 4000.
Similarly, the cost for 350 units is Rs. 5000:
C(350) = 5000.
Now, let's find the slope (rate of change) of the cost function using the given data:
Slope = (5000 - 4000) / (350 - 250) = 1000/100 = 10.
Now, the general form of a linear cost function is C(x) = mx + b, where m is the slope and b is the y-intercept. So, the cost function is:
C(x) = 10x + b.
To find the value of b, we can use one of the data points. Let's use C(250) = 4000:
4000 = 10 * 250 + b
4000 = 2500 + b
b = 1500.
Therefore, the cost function is:
C(x) = 10x + 1500.
Now, let's compare this with the given options:
a) C(x) = 20x + 3000
b) C(x) = 10x + 2500 (Matches)
c) C(x) = 15x + 2500
d) C(x) = 20x + 2500
If costs are Rs. 4000 for 250 units and Rs. 5000 for 350 units are sold The cost function is b) C(x) = 10x + 2500.