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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) = 1 5700x Find the cost function, C(x), in dollars. C(x) = 3020x + 2x Find the profit function, P(x), in dollars. 3 – 2x2 + 2680x P(x) Find P'(x). 3 2 P'(x) = 4x + 2680 2 Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) 49.80 X units Find the maximum profit. (Round your answer to the nearest cent.) $ 66738.50 Does the maximum profit result in a profit or loss? profit loss

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) = 1 5700x Find the cost function, C(x), in dollars. C(x) = 3020x + 2x Find the profit function, P(x), in dollars. 3 – 2x2 + 2680x P(x) Find P'(x). 3 2 P'(x) = 4x + 2680 2 Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) 49.80 X units Find the maximum profit. (Round your answer to the nearest cent.) $ 66738.50 Does the maximum profit result in a profit or loss? profit loss

Calculus: Early Transcendentals
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) = 1 5700x Find the cost function, C(x), in dollars. C(x) = 3020x + 2x Find the profit function, P(x), in dollars. 3 – 2x2 + 2680x P(x) Find P'(x). 3 2 P'(x) = 4x + 2680 2 Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) 49.80 X units Find the maximum profit. (Round your answer to the nearest cent.) $ 66738.50 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) = 1 5700x Find the cost function, C(x), in dollars. C(x) = 3020x + 2x Find the profit function, P(x), in dollars. 3 – 2x2 + 2680x P(x) Find P'(x). 3 2 P'(x) = 4x + 2680 2 Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) 49.80 X units Find the maximum profit. (Round your answer to the nearest cent.) $ 66738.50 Does the maximum profit result in a profit or loss? profit loss
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