Answer:
The correct answer is 10 for lowest average cost and the cost function is 0.2[tex]x^{2}[/tex] + 75x + 20.
Step-by-step explanation:
Average cost function is given by = [tex]\frac{Cost}{Quantity}[/tex] = C(x) = 0.2x + [tex]\frac{20}{x}[/tex] +75.
For minimizing we need to find [tex]\frac{d}{dx}[/tex]C(x) = 0.
⇒ [tex]\frac{d}{dx}[/tex]C(x) = 0.2 - [tex]\frac{20}{x^{2}}[/tex].
⇒ [tex]\frac{20}{x^{2}}[/tex] = 0.2
⇒ [tex]x^{2}[/tex] = 100.
⇒ x = ±10
⇒ x = 10 ; cost cannot be negative.
Second order derivative is positive which implies the average cost minimizes.
Original cost function is given by C(x) × x = 0.2[tex]x^{2}[/tex] + 75x + 20.
