(3) The demand curve of a firm is p=1200 – 2 lq and its total cost is C(q) = 2q° – 66q² +600g +1000 where q is the output of the firm (in thousands). (i) Derive an expression R(q), for the firm' s revenue function. (ii) Derive an expression II(g) for the firm' s profit function. (iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10,000 units? (iv) Determine the level of output at which profit is maximized.
(3) The demand curve of a firm is p=1200 – 2 lq and its total cost is C(q) = 2q° – 66q² +600g +1000 where q is the output of the firm (in thousands). (i) Derive an expression R(q), for the firm' s revenue function. (ii) Derive an expression II(g) for the firm' s profit function. (iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10,000 units? (iv) Determine the level of output at which profit is maximized.
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 – 2 lq and its total cost is
C(q) = 2q° – 66q² +600g +1000 where q is the output of the firm (in thousands).
(i)
Derive an expression R(q), for the firm' s revenue function.
(ii)
Derive an expression II(g) for the firm' s profit function.
(iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is
10,000 units?
(iv) Determine the level of output at which profit is maximized.
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