A product costs the manufacturer ₹20 per unit. The demand function is given by $p(x) = 1000 - 20x$, then the quantity for maximum profit is:

$\frac{49}{2}$ units

The correct answer is Option (4) - $\frac{49}{2}$ units

$\text{Cost per unit} = 20 \Rightarrow C(x) = 20x$

$\text{Demand function} \; p(x) = 1000 - 20x$

$\text{Revenue } R(x) = x \cdot p(x) = x(1000 - 20x)$

$= 1000x - 20x^2$

$\text{Profit } P(x) = R(x) - C(x)$

$= (1000x - 20x^2) - 20x$

$= 980x - 20x^2$

$\frac{dP}{dx} = 980 - 40x$

$980 - 40x = 0$

$x = \frac{980}{40} = 24.5$

The quantity for maximum profit is $24.5$ units.