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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) = 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

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

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 88E
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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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