Question

A manufacturer produces 80 TV sets at a cost of ₹ 2,20,000 and 125 TV sets at a cost of ₹ 2,87,500. Assuming the cost curve to be linear, find the linear expression of the given information. Also, estimate the cost of 95 TV sets.

Answer 1

Let x represent the TV sets, andy represent the cost.

TV (x)	Cost (y)
80 (x1)	2,20,000
125 (x2)	2,87,500

The equation of straight line expressing the given information as a linear equation in x and y is

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

`(y - 2,20,000)/(2,87,500 - 2,20,000) = (x - 80)/(125 - 80)`

`(y - 2,20,000)/(67,500) = (x - 80)/45`

`(y - 2,20,000)/(1,500) = (x - 80)/1`

1(y – 2,20,000) = (x – 80)1500

y – 2,20,000 = 1500x – 80 × 1500

y = 1500x – 1,20,000 + 2,20,000

y = 1500x + 1,00,000 which is the required linear expression.

When x = 95,

y = 1,500 × 95 + 1,00,000

= 1,42,500 + 1,00,000

= 2,42,500

∴ The cost of 95 TV sets is ₹ 2,42,500.