Question

A company is selling a certain commodity ‘x’. The demand function for the commodity is linear. The company can sell 2000 units when the price is Rs. 8 per unit and it can sell 3000 units when the price is Rs. 4 per unit. The Marginal revenue at x = 5 is:

• A. Rs. 79.98
• B. Rs. 15.96
• C. Rs. 16.04
• D. Rs. 80.02

Answer 1

Answer: (B)

Rs. 15.96

Answer 2

The demand function $p(x)$ is linear. Using the points $(2000, 8)$ and $(3000, 4)$, find the slope $m$ and intercept $c$:

$m = \frac{4 - 8}{3000 - 2000} = \frac{-4}{1000} = -0.004, \quad c = 8 + 2000(0.004) = 16.$

Thus, $p(x) = -0.004x + 16$. Revenue $R(x)$ is:

$R(x) = x \cdot p(x) = x(-0.004x + 16) = -0.004x^2 + 16x.$

The Marginal Revenue is:

$R'(x) = -0.008x + 16.$

At $x = 5$:

$R'(5) = -0.008(5) + 16 = -0.04 + 16 = 15.96.$