Calculating Marginal Cost from Total Cost Function

The question provides the total cost function and asks for the marginal cost (MC) at a specific price. We first need to find the marginal cost function.

Step 1: Find the Marginal Cost (MC) Function

Marginal Cost is the derivative of the Total Cost (C) function with respect to Quantity (Q).

Given Total Cost function: $C = 5Q^2 + 20Q + 5$

Differentiate C with respect to Q to find MC: $MC = \frac{dC}{dQ} = \frac{d}{dQ}(5Q^2 + 20Q + 5)$ $MC = 10Q + 20$

Step 2: Determine the Quantity (Q) for MC Calculation

The question states the price is ₹ 5. In microeconomics, firms typically produce where Price (P) equals Marginal Cost (MC). However, the derived MC function starts at ₹ 20 (for $Q > 0$) and increases. A price of ₹ 5 would imply zero production, which contradicts the provided options.

Given the options, especially ₹ 70, let's check the quantity (Q) that yields MC = ₹ 70:

Setting $MC = 70$: $70 = 10Q + 20$ $10Q = 70 - 20$ $10Q = 50$ $Q = 5$

This suggests the question implicitly relates to the scenario where the quantity produced is Q=5, despite the potentially misleading price information.

Step 3: Calculate Marginal Cost at Q=5

Substitute Q=5 into the marginal cost function:

$MC = 10(5) + 20$ $MC = 50 + 20$ $MC = 70$

Therefore, the marginal cost is ₹ 70.