Question

ssume that the cost of producing n pair of shoes is given by C(n)=4n(1/2)+3n2. The marginal cost of producing shoes at n is the derivative of C at n. What is the expression of the marginal cost of producing shoes at n?

Answer 1

Answer: The expression of the marginal cost of producing shoes at n would be :
`2n^{(-1)/(2)}+6n`

Explanation:

Given : The cost of producing n pair of shoes is given by

`C(n)=4n^{(1)/(2)}+3n^2`

Since , the marginal cost of producing shoes at n is the derivative of C at n.

Therefore , Marginal cost function =
`C'(n)=4 ((1)/(2)n^{(1)/(2)}-1)+3(2n)\ \ [\because\ (d\ x^m)/(dx)=mx^(m-1)]`

`=2n^{(-1)/(2)}+6n`

Hence, the expression of the marginal cost of producing shoes at n would be :
`2n^{(-1)/(2)}+6n`