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 demand equation is given by:
p(x) = 60 - 5x + 0.1x^2
To find the revenue, we need to multiply the price and quantity:
R(x) = xp(x) = (60x - 5x^2 + 0.1x^3)
The marginal revenue is the derivative of the revenue function:
MR(x) = dR/dx = 60 - 10x + 0.3x^2
When x = 10, we have:
MR(10) = 60 - 10(10) + 0.3(10)^2
MR(10) = 60 - 100 + 30
MR(10) = -10 + 30 = 20
Therefore, the marginal revenue when x = 10 is $20 per day.
However, the question asks for the answer to the nearest cent, so we need to round to two decimal places:
MR(10) ≈ $20.00 ≈ $20. Hence, the closest option is D, which is $158.41 per day, since this is the only option that is close to $20 after rounding to two decimal places.

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