Question

Suppose a product's revenue function is given by R(q)=-5 q^{2}+700 q Find an expression for the marginal revenue function, simplify it.

Answer 1

The marginal revenue function MR(q) is derived by differentiating the revenue function R(q) = -5q^2 + 700q, which gives MR(q) = -10q + 700.

Step-by-step explanation:

The student asked for an expression of the marginal revenue function based on the given revenue function R(q) = -5q2 + 700q. To find the marginal revenue function, we differentiate the revenue function with respect to quantity q.

The marginal revenue function MR(q) is the derivative of the revenue function, which can be calculated as follows:

1. Take the derivative of -5q2, which is -10q.
2. Take the derivative of 700q, which is 700.

Combining these results, the marginal revenue function is MR(q) = -10q + 700.

This simplified expression shows that for every additional unit sold, the revenue is expected to increase by the value of MR(q) at that specific quantity.