Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(II), (B)-(III), (C)-(I), (D)-(IV)

The correct answer is Option (3) → (A)-(II), (B)-(III), (C)-(I), (D)-(IV)

(A) Marginal average cost if $C(x)=\frac{50}{\sqrt{x}}$

Average cost = $\frac{C(x)}{x}=\frac{50}{x\sqrt{x}}=\frac{50}{x^{3/2}}$

Marginal average cost = derivative:

$\frac{d}{dx}\left(\frac{50}{x^{3/2}}\right)= -\frac{75}{x^{5/2}}$

Matches (II) $\; -\frac{75}{x^2\sqrt{x}}$

(B) Marginal average cost if $C(x)=50\sqrt{x}$

Average cost = $\frac{50\sqrt{x}}{x}=\frac{50}{\sqrt{x}}$

Marginal average cost = derivative:

$\frac{d}{dx}\left(\frac{50}{\sqrt{x}}\right)= -\frac{25}{x^{3/2}}$

Matches (III) $\; -\frac{25}{x\sqrt{x}}$

(C) Revenue when $P=\frac{50}{\sqrt{x}}$

$R(x)=xP=x\cdot\frac{50}{\sqrt{x}}=50\sqrt{x}$

Matches (I) $50\sqrt{x}$

(D) Marginal revenue when $P=50\sqrt{x}$

$R(x)=x\cdot 50\sqrt{x}=50x^{3/2}$

$R'(x)=75\sqrt{x}$

Matches (IV) $75\sqrt{x}$

The correct matching is: A–II, B–III, C–I, D–IV.