Marginal Revenue

Question

Marginal Revenue

The demand function for a certain boat company's 34 ft Sundancer yacht is

p = 400 − 0.01x ln(x)

where x denotes the number of yachts and p is the price per yacht in hundreds of dollars.

(a)

Find the revenue function R(x) and the marginal revenue function R'(x) for this model of yacht.

R(x) =400x-0.01x^2ln(x)

R'(x) =-0.02xln(x)-0.01x+400

(b)

Use the result of part (a) to estimate the revenue to be realized from the sale of the 400^th 34 ft Sundancer yacht. (Round your answer to the nearest dollar.)

$______

Answer 1

Hello Ryan,

Your answers for part a look good!

R '(x) gives the rate of change in revenue which is the increase in revenue which would be about the same as the money that came in from selling the newest item. So figure out R '(400). See if you can work out the final answer with a calculator.