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The demand curve of a firm is p = 1200 - 21q and its total cost is C(q) = 2q3-66q 2 +600q + 1000 where q is the output of the firm (in thousand)  (i) Derive an expression R(q) for the firm's revenue function  (ii) Derive an expression (q ) for the firm's profit function  (iii) Is the rate of exchange of profit increasing or decreasing when the output level of the firm is 10,000 units? (iv) Determine the level of ouput at whihc profit is maximised

The demand curve of a firm is p = 1200 - 21q and its total cost is C(q) = 2q3-66q 2 +600q + 1000 where q is the output of the firm (in thousand)  (i) Derive an expression R(q) for the firm's revenue function  (ii) Derive an expression (q ) for the firm's profit function  (iii) Is the rate of exchange of profit increasing or decreasing when the output level of the firm is 10,000 units? (iv) Determine the level of ouput at whihc profit is maximised

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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The demand curve of a firm is p = 1200 - 21q and its total cost is C(q) = 2q3-66q 2 +600q + 1000 where q is the output of the firm (in thousand) 

(i) Derive an expression R(q) for the firm's revenue function 

(ii) Derive an expression (q ) for the firm's profit function 

(iii) Is the rate of exchange of profit increasing or decreasing when the output level of the firm is 10,000 units?

(iv) Determine the level of ouput at whihc profit is maximised 

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