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A polluting factory produces emissions whose damage (D) declines with distance. Robin works in, this factory. The damage to Robin is D (r) = 1000/r, where r is distance in kilometer from the firm and D is damage in rupees. His cost of commuting from the factory to home is 20 per km. (i) Write an expression for Robin's total cost. (ii) At what distance from the factory will Robin live? (If he wants to minimize his total cost.) (iii) At what distance from the factory will Robin live if he receives full compensation for the damage he incurs? The minimum distance from the factory where the Robin can live is 0.2 kilometers.

A polluting factory produces emissions whose damage (D) declines with distance. Robin works in, this factory. The damage to Robin is D (r) = 1000/r, where r is distance in kilometer from the firm and D is damage in rupees. His cost of commuting from the factory to home is 20 per km. (i) Write an expression for Robin's total cost. (ii) At what distance from the factory will Robin live? (If he wants to minimize his total cost.) (iii) At what distance from the factory will Robin live if he receives full compensation for the damage he incurs? The minimum distance from the factory where the Robin can live is 0.2 kilometers.

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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A polluting factory produces emissions whose damage (D) declines with distance. Robin works in this factory. The damage to Robin is D (r) = 1000/r, where r is distance in kilometer from the firm and D is damage in rupees. His cost of commuting from the factory to home is 20 per km. (i) Write an expression for Robin's total cost. (ii) At what distance from the factory will Robin live? (If he wants to minimize his total cost.) (iii) At what distance from the factory will Robin live if he receives full compensation for the damage he incurs? The minimum distance from the factory where the Robin can live is 0.2 kilometers. (8)
Transcribed Image Text:A polluting factory produces emissions whose damage (D) declines with distance. Robin works in this factory. The damage to Robin is D (r) = 1000/r, where r is distance in kilometer from the firm and D is damage in rupees. His cost of commuting from the factory to home is 20 per km. (i) Write an expression for Robin's total cost. (ii) At what distance from the factory will Robin live? (If he wants to minimize his total cost.) (iii) At what distance from the factory will Robin live if he receives full compensation for the damage he incurs? The minimum distance from the factory where the Robin can live is 0.2 kilometers. (8)
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