Question

Suppose the cost to produce some commodity is a linear function of cost as a function of output. If costs are Rs. 4000 for 250 units and Rs. 5000 for 350 units are sold? a) The cost function is C(x) = 20x + 3000. b) The cost function is C(x) = 10x + 2500. c) The cost function is C(x) = 15x + 2500. d) The cost function is C(x) = 20x + 2500.

Answer 1

The cost function is C(x) = 10x + 2500.

Step-by-step explanation:

In this question, we are given the cost of producing a commodity for two different quantities: Rs. 4000 for 250 units and Rs. 5000 for 350 units. We need to determine the cost function.

To find the cost function, we need to determine the slope (rate of change) of the cost as a function of output. We can do this by taking the difference in costs and dividing it by the difference in output: (5000 - 4000) / (350 - 250) = 1000 / 100 = 10.

Therefore, the cost function is given by C(x) = 10x + b, where x is the quantity of output and b is the y-intercept. We can determine the value of b by substituting the values of x and C(x) from one of the given points (250, 4000 or 350, 5000) into the equation and solving for b. By substituting the values (250, 4000), we get 4000 = 10 * 250 + b, which gives b = 2500.

Therefore, the cost function is C(x) = 10x + 2500. Option b) is the correct answer.

Answer 2

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.