Question

As the number of units produced increases from 500 to 1000 and the total cost of production increases from ₹ 6000 to ₹ 9000. Find the relationship between the cost (y) and the number of units produced (x) if the relationship is linear.

Answer 1

Let x and y represent the number of units produced and the cost of production respectively. By the given data.

x₁ (500)   y₁ (6000)
x₂ (1000)   y₂ (9000)

Using two point form, the relationship between x and y is

`(y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1)`

`=> (y - 6000)/(9000 - 6000) = (x - 500)/(1000 - 500)`

`=> (y - 6000)/(3000) = (x - 500)/(500)`

`=> (y - 6000)/(6) = (x - 500)/(1)`

⇒ y - 6000 = 6(x - 500)

⇒ y - 6000 = 6x - 3000

⇒ y = 6x - 3000 + 6000

⇒ y = 6x + 3000