Answer:
x = 50
Explanation:
Given that,
The total cost of production of spare parts of computer is given as
C=4000x-100x²+x³
Where x is the number of units of spare parts produced
We need to find the number of units of spare parts so that the average cost will be maximum.
Average cost,
[tex]C(x)=\dfrac{C}{x}\\\\=\dfrac{4000x-100x^2+x^3}{x}\\\\=4000-100x+x^2[/tex]
For maximum average cost, put d(c)/dx = 0
[tex]\dfrac{d(4000-10x+x^2)}{dx}=0\\\\-100+2x=0\\\\x=50[/tex]
So, the number of units of spare parts is 50.
