The average cost function of producing and marketing 'x' units is given by $AC=2 x-20+\frac{50}{x}$. Then the value of the output x, for which the total cost is increasing is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → x > 5
$AC = 2x - 20 + \frac{50}{x}$
$\text{Total cost } TC = x \cdot AC$
$TC = x\left(2x - 20 + \frac{50}{x}\right)$
$TC = 2x^2 - 20x + 50$
$\frac{d(TC)}{dx} = 4x - 20$
$TC \text{ is increasing when } \frac{d(TC)}{dx} > 0$
$4x - 20 > 0$
$x > 5$
The total cost is increasing for $x > 5$.