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A firm's price in a perfectly competitive market is 1000. Its cost function is C(x) = 0.01x³ 3x² +1108x +960, where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function 7(x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. (c) Using a sign diagram, determine the intervals over which 7(x) is increasing and decreasing. (d) Determine the intervals over which 7(x) is concave and convex. (e) Where is the point of inflection in C(x) ? Give an economic interpretation of the point of inflection.

A firm's price in a perfectly competitive market is 1000. Its cost function is C(x) = 0.01x³ 3x² +1108x +960, where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function 7(x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. (c) Using a sign diagram, determine the intervals over which 7(x) is increasing and decreasing. (d) Determine the intervals over which 7(x) is concave and convex. (e) Where is the point of inflection in C(x) ? Give an economic interpretation of the point of inflection.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 5 A firm's price in a perfectly competitive market is 1000. Its cost function is C(x) = 0.01x³ – 3x² + 1108x + 960, where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function (x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. (c) Using a sign diagram, determine the intervals over which (x) is increasing and decreasing. (d) Determine the intervals over which 7(x) is concave and convex. (e) Where is the point of inflection in C(x) ? Give an economic interpretation of the point of inflection.
Transcribed Image Text:Question 5 A firm's price in a perfectly competitive market is 1000. Its cost function is C(x) = 0.01x³ – 3x² + 1108x + 960, where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function (x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. (c) Using a sign diagram, determine the intervals over which (x) is increasing and decreasing. (d) Determine the intervals over which 7(x) is concave and convex. (e) Where is the point of inflection in C(x) ? Give an economic interpretation of the point of inflection.
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