Question

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 so that the average cost will be maximum?

Answer 1

x = 50

Step-by-step 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,

`C(x)=(C)/(x)\\\\=(4000x-100x^2+x^3)/(x)\\\\=4000-100x+x^2`

For maximum average cost, put d(c)/dx = 0

`(d(4000-10x+x^2))/(dx)=0\\\\-100+2x=0\\\\x=50`

So, the number of units of spare parts is 50.