Question

In Shraddha's Farm the cost of function for output x is given by C = x ^2/3 - 20x^2 + 70x. Find the output for which i) Marginal cost is minimum, ii) Average cost is minimum


PLEASE SOLVE THISS​

Answer 1

Average cost ( CA) = C / x

So, it would be = x^3 /3 - 20x^2 + 70x / x

CA = x ( x^2 / 3 - 20x + 70 ) / x

Both x will be cancelled

CA = ( x^2 / 3 - 20x + 70 )

Now differentiate with respect to x

dCA / dx = 1/3 ( 2x ) - 20

= 2/3 x - 20

Since , dCA / dx > 0 ( Minimum )

Now ,

2/3 x - 20 > 0

2/3 x > 20

x > 20 × 3 / 2

x > 30

The average cost CA is minimum for x > 30.