The unit selling price p (in dollars) and the quantity demanded (in pairs) of a certain brand of women's gloves is given by the demand equation . What is the marginal revenue to the nearest cent per day when x = 10?
A) The marginal revenue when x = 10 is $160 per day.
B) The marginal revenue when x = 10 is $147.41 per day.
C) The marginal revenue when x = 10 is $0.99 per day.
D) The marginal revenue when x = 10 is $158.41 per day.

Question

The unit selling price p (in dollars) and the quantity demanded (in pairs) of a certain brand of women's gloves is given by the demand equation  . What is the marginal revenue to the nearest cent per day when x = 10?
A) The marginal revenue when x = 10 is $160 per day. 
B) The marginal revenue when x = 10 is $147.41 per day. 
C) The marginal revenue when x = 10 is $0.99 per day. 
D) The marginal revenue when x = 10 is $158.41 per day.

Quizplus · Accepted Answer

The marginal revenue (MR) is the derivative of the revenue function with respect to x.

The revenue function is given by:

R(x) = x(p(x)) = x(40 - 3ln(x))

Taking the derivative with respect to x:

MR = R'(x) = p(x) + x(p'(x))

where p(x) is the price function and p'(x) is the derivative of the price function.

p(x) = 40 - 3ln(x)

p'(x) = -3/x

MR = (40 - 3ln(x)) + x(-3/x)

When x = 10,

MR = (40 - 3ln(10)) - 3

MR ≈ $158.41 per day

Therefore, the best choice is D, as it is the closest to the calculated value.

The Unit Selling Price P (In Dollars) and the Quantity