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The total revenue curve of a firm is R(q) = 40q − 12q2 and its  average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q ,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?

The total revenue curve of a firm is R(q) = 40q − 12q2 and its  average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q ,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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The total revenue curve of a firm is R(q) = 40q − 12q2 and its  average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q ,where q is the firms output.

i. Derive an expression C(q) for the firms total cost function.

ii. Derive an expression Π(q) for the firms profit function.

iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units?

iv. Determine the level of output for which the firms profit is maximized.

v. What is the firmss maximum profit?

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