Assume that the total revenue (in dollars) from the sale of x television sets is

Question

Assume that the total revenue (in dollars) from the sale of x television sets is given by R(x) = 24(x^2 + x)^2/3. Find the marginal revenue when the following numbers of sets are sold. a. 100 b. 200 c. 300 d. Find the average revenue from the sale of x sets. e. Find the marginal average revenue. f. Write a paragraph covering the following questions. How does the revenue change over time? What does the marginal revenue function tell you about the revenue function? What does the average revenue function tell you about the revenue function?

Explanation / Answer

given revenue R(x)=24(x2+x)2/3

a) marginal revenue M=dR/dx

M=24(2/3)(x2+x)(2/3)-1(2x +1)

M=16(2x +1)(x2+x)(-1/3)

x =100

M=16(2*100 +1)(1002+100)(-1/3)

M=148.8

marginal revenue =148.8 dollars

b)x=200 units

M=16(2*200 +1)(2002+200)(-1/3)

marginal revenue =187.3 dollars

c)

x=300 units

M=16(2*300 +1)(3002+300)(-1/3)

marginal revenue =214.3 dollars

d)average revenue A=(R(x))/x

A=(24(x2+x)2/3)/x

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