The demand function for a commodity is $p= 35-2x-x^2$, then the consumer's surplus at equilibrium price $p_0 = 20$ is

27

The correct answer is Option (3) → 27 **

Demand function: $p = 35 - 2x - x^{2}$

Equilibrium price: $p_{0} = 20$

Find equilibrium quantity:

$20 = 35 - 2x - x^{2}$

$x^{2} + 2x - 15 = 0$

$x = 3$ (positive root)

Consumer surplus:

$CS = \int_{0}^{3} (35 - 2x - x^{2})\,dx - p_{0}x_{0}$

$\int (35 - 2x - x^{2})\,dx = 35x - x^{2} - \frac{x^{3}}{3}$

Evaluate from $0$ to $3$:

$= 35(3) - 9 - \frac{27}{3}$

$= 105 - 9 - 9$

$= 87$

Now subtract $p_{0}x_{0} = 20 \times 3 = 60$

$CS = 87 - 60 = 27$

The consumer’s surplus is $27$.