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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.