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R ( x ) = 500 x ? x 2 dollars where x denotes the number of units sold. (a) What

ID: 3374398 • Letter: R

Question

R(x) = 500x ? x2 dollars where x denotes the number of units sold. (a) What is the function that gives marginal revenue?
R'(x) =

(b) What is the marginal revenue if 50 units are sold?
R'(50) =

What does it mean? R(x) is decreasing.R(x) is constant.    R(x) is increasing.
(c) What is the marginal revenue if 350 units are sold?
R'(350) =

What does it mean? R(x) is decreasing.R(x) is constant.    R(x) is increasing.
(d) What is the marginal revenue if 250 units are sold?
R'(250) =

(e) As the number of units sold passes through 250, what happens to revenue? The revenue changes from increasing to decreasing.The revenue changes from decreasing to increasing. R(x) = 500x ? x2 dollars R(x) = 500x ? x2 dollars (a) What is the function that gives marginal revenue?
R'(x) =

(b) What is the marginal revenue if 50 units are sold?
R'(50) =

What does it mean? R(x) is decreasing.R(x) is constant.    R(x) is increasing.
(c) What is the marginal revenue if 350 units are sold?
R'(350) =

What does it mean? R(x) is decreasing.R(x) is constant.    R(x) is increasing.
(d) What is the marginal revenue if 250 units are sold?
R'(250) =

(e) As the number of units sold passes through 250, what happens to revenue? The revenue changes from increasing to decreasing.The revenue changes from decreasing to increasing. R'(x) = R'(50) = R(x) is decreasing.R(x) is constant.    R(x) is increasing. R'(350) = R(x) is decreasing.R(x) is constant.    R(x) is increasing. R'(250) = The revenue changes from increasing to decreasing.The revenue changes from decreasing to increasing.

Explanation / Answer

a)

R'(x) = 500 - 2x

b)

R'(50) = 500-100 = 400 > 0 -> R(x) is increasing

c)

R'(350) = 500-700 = -200 < 0 -> R(x) is decreasing

d)

R'(250) = 0

e)

250 is maximum point -> passes from 250 -> R(x) decreases