A manufacturer produces 80 units of a product at a cost of Rs 22000 and 125 units at a cost of Rs 28750. Assuming the cost curve to be linear, find the equation of the cost curve and then use it to estimate the cost of 95 units.

Given:

The total cost of 80 units of a product at a cost of Rs 22000 and 125 units at a cost of Rs 28750.

To do:

We have to find the cost of 95 units.

Solution:

The cost curve is linear.

Let its equation will be $y = Ax + B$, where $y =$ Total cost and $x =$ Number of units.

This implies,

$22000  =  80A + B$

$80A + B  =  22000$.........(i)

$28750  =  125A + B$

$125A + B  =  28750$.........(ii)

Solving (i) and (ii), we get,

$125A+B-80A-B=28750-22000$

$45A=6750$

$A=\frac{6750}{45}$

$A=150$

$\Rightarrow 80(150)+B =22000$

$B=22000-12000$

$B=10000$

Therefore, the equation of the cost curve is $y = 150x + 10000$..........(iii)

This implies, the cost of 95 units is,

$y  =  150(95) + 10000$

$y  =  14250 + 10000$

$y  =  24250$

Hence, the cost of 95 units is Rs. 24250.