The monthly demand function for x units of a product sold by a monopoly is p = 5,700 – x² dollars, and its average cost is C = 3,020 + 2x dollars. Production is limited to 100 units. Find the revenue function, R(x), in dollars. R(x) = Find the cost function, C(x), in dollars. C(x) = %3D Find the profit function, P(x), in dollars. P(x) = Find P'(x). P'(x) Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) units Find the maximum profit. (Round your answer to the nearest cent.) $ Does the maximum profit result in a profit or loss? profit loss

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The monthly demand function for x units of a product sold by a monopoly is

p = 5,700 − 
1
2
x2 dollars,

and its average cost is

C = 3,020 + 2x dollars.

Production is limited to 100 units.

The monthly demand function for x units of a product sold by a monopoly is p = 5,700 – x² dollars, and its average cost is C = 3,020 + 2x dollars. Production is limited to 100 units.
Find the revenue function, R(x), in dollars.
R(x) =
Find the cost function, C(x), in dollars.
C(x) =
%3D
Find the profit function, P(x), in dollars.
P(x) =
Find P'(x).
P'(x)
Find the number of units that maximizes profits. (Round your answer to the nearest whole number.)
units
Find the maximum profit. (Round your answer to the nearest cent.)
$
Does the maximum profit result in a profit or loss?
profit
loss
Transcribed Image Text:The monthly demand function for x units of a product sold by a monopoly is p = 5,700 – x² dollars, and its average cost is C = 3,020 + 2x dollars. Production is limited to 100 units. Find the revenue function, R(x), in dollars. R(x) = Find the cost function, C(x), in dollars. C(x) = %3D Find the profit function, P(x), in dollars. P(x) = Find P'(x). P'(x) Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) units Find the maximum profit. (Round your answer to the nearest cent.) $ Does the maximum profit result in a profit or loss? profit loss
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