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. In a simple model of territory, a single animal defends a circular territory of radius x (miles). The following assumptions are made: • the energy L spent per day in looking for food and defending the territory is directly proportional to the area of the region • the energy G gained per day is directly proportional to the radius x Suppose that L = 3000 calories and G = 3500 calories when x 1. Find the territorial size that will result in maximum benefit to the animal, that is, maximize the net energy G- L.

. In a simple model of territory, a single animal defends a circular territory of radius x (miles). The following assumptions are made: • the energy L spent per day in looking for food and defending the territory is directly proportional to the area of the region • the energy G gained per day is directly proportional to the radius x Suppose that L = 3000 calories and G = 3500 calories when x 1. Find the territorial size that will result in maximum benefit to the animal, that is, maximize the net energy G- L.

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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5. In a simple model of territory, a single animal defends a circular territory of radius x (miles). The following assumptions are made: • the energy L spent per day in looking for food and defending the territory is directly proportional to the area of the region • the energy G gained per day is directly proportional to the radius x Suppose that L = 3000 calories and G = 3500 calories when x = 1. Find the territorial size that will result in maximum benefit to the animal, that is, maximize the net energy G- L.
Transcribed Image Text:5. In a simple model of territory, a single animal defends a circular territory of radius x (miles). The following assumptions are made: • the energy L spent per day in looking for food and defending the territory is directly proportional to the area of the region • the energy G gained per day is directly proportional to the radius x Suppose that L = 3000 calories and G = 3500 calories when x = 1. Find the territorial size that will result in maximum benefit to the animal, that is, maximize the net energy G- L.
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