The marginal revenue of a company is given by R'(x) = 100 + 20x + 3x2, %3D where x is amount of units sold for a period. Find the total revenue function if at x = 2, the total revenue is equal to 260.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Do c) only. 

(c) The marginal revenue of a company is given by
R'(x) = 100 + 20x + 3x2,
where x is amount of units sold for a period. Find the total revenue function if at
x = 2, the total revenue is equal to 260.
Transcribed Image Text:(c) The marginal revenue of a company is given by R'(x) = 100 + 20x + 3x2, where x is amount of units sold for a period. Find the total revenue function if at x = 2, the total revenue is equal to 260.
(a) Suppose that
c(x) = x³ – 20x? + 20, 000x
%3D
is the cost of manufacturing x items. Find a production level that will minimize the
average cost of making x items.
(b) It costs you c dollars each to manufacture and distribute backpacks. If the backpacks
sell at x dollars each, the number sold is given by
a
n =
+ b(100 – 2),
I — с
where a and b are positive constants. What selling price will bring a maximum profit?
(Hint: the profit is p = nx – cz)
Transcribed Image Text:(a) Suppose that c(x) = x³ – 20x? + 20, 000x %3D is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items. (b) It costs you c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars each, the number sold is given by a n = + b(100 – 2), I — с where a and b are positive constants. What selling price will bring a maximum profit? (Hint: the profit is p = nx – cz)
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