The cost function for a product in a firm is given by $5q^2$, where $q$ is the amount of production. The firm can sell the product at a market price of ₹ $50$ per unit. The number of units to be produced by the firm such that the profit is maximized is

Let the total revenue be $R(q)$ and the total cost be $C(q)$.

• Selling price per unit = ₹ $50$

• Total Revenue: $R(q) = 50q$

• Total Cost: $C(q) = 5q^2$

The profit function $P(q)$ is:

To find the value of $q$ that maximizes profit, find the critical points:

Check the second derivative for maximization:

Since the second derivative is negative, profit is maximized at $q = 5$.

Hence, the correct option is (A).