Question

Q.16. The total cost functions for producing a commodity in \( x \) quantity is T.C \( =60-12 x+2 x^{2} \). (a) Find the average cost functions. (b) The level of output at which this function is minimum.

Answer 1

(a) T.C = 60 - 12x - 2x²

Average cost = \(\frac {T.C.}x = \frac {60 + 2x - 2x^2}x\) 

(b) \(f(x) = 60 - 12x + 2x^2\)

\(f'(x) = -12 + 4x\)

\(f'(x) = 0 \) gives -12 + 4x = 0 

⇒ \(x = \frac {12}{+4} = +3\) 

\(f''(x) = + 4 > 0\)

Hence, x = 3 is point of minima.

Hence, at x = 3, the function is minimum.