Question

The average cost function associated with producing and marketing x units of an item is given by AC = 2x – 11 + (50/x). Find the range of values of the outputx, for which AC is increasing.

Answer 1

The average cost function associated with producing and marketing x units of an item is given as: 

AC = 2x – 11 + (50/x)

Output’for which AC increases is: 

(d/dx) (AC) > 0 

⇒ (d/dx) (2x – 11 + (50/x)) > 0 

⇒ 2 - (50/x²) > 0

⇒ x² – 25 > 0 

⇒ (x – 5)(x + 5) > 0 

⇒ x > 5 [∵ x > 0] 

Clearly, the average cost increases, if the output x > 5.