Question

The price per unit of a commodity produced by a company is given by P = 92 - 2x², where x is the quantity demanded. The marginal revenue of producing 3 units of such a commodity shall be :

• A. 28
• B. 38
• C. 26
• D. 44

Answer 1

The Correct Option is B

To find the marginal revenue of producing 3 units of the commodity, we start by understanding the given price function and the relationship between price and revenue.

The price per unit, P, is given by:

P=92-2x^2

Where x represents the quantity demanded. The revenue, R(x), is given by the formula:

R(x)=P*x=(92-2x^2)x=92x-2x^3

The marginal revenue is the derivative of the revenue function, R(x), with respect to x. So, we need to compute:

R'(x)=d/dx(92x-2x^3)

By applying the power rule, the derivative is:

R'(x)=92-6x^2

Now, evaluate the marginal revenue when x=3:

R'(3)=92-6(3)^2=92-54=38

Thus, the marginal revenue of producing 3 units is 38. The correct answer is therefore 38.