Consider a situation where there are bears around your campus. Since bears harm our campus life, a student group decides to remove bears from the mountain behind the campus. The removal cost is described by: C(y, x) = | (z)dz, x-y where x is the number of existing bears before removals, and y is the number of removals such that 0 < y 0 and 0 1) represents how easy you can catch a bear in the field of biology. Find the total cost of eradication of bears (i.e., y = x) as a function of x and 0. Show that if 0 > 1, the student group cannot achieve the eradication of bears.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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calculus

Consider a situation where there are bears around your campus. Since bears harm our campus life, a student
group decides to remove bears from the mountain behind the campus. The removal cost is described by:
C(y, x) = | c(2)dz,
x-y
where x is the number of existing bears before removals, and y is the number of removals such that 0 < y< x.
The function c(2) is a sort of the unit cost function, which is simply specified as c(2) = x¯°, where the pa-
rameter 0 (0 > 0 and 0 7 1) represents how easy you can catch a bear in the field of biology. Find the total
cost of eradication of bears (i.e., y = x) as a function of x and 0. Show that if 0 > 1, the student group
cannot achieve the eradication of bears.
Transcribed Image Text:Consider a situation where there are bears around your campus. Since bears harm our campus life, a student group decides to remove bears from the mountain behind the campus. The removal cost is described by: C(y, x) = | c(2)dz, x-y where x is the number of existing bears before removals, and y is the number of removals such that 0 < y< x. The function c(2) is a sort of the unit cost function, which is simply specified as c(2) = x¯°, where the pa- rameter 0 (0 > 0 and 0 7 1) represents how easy you can catch a bear in the field of biology. Find the total cost of eradication of bears (i.e., y = x) as a function of x and 0. Show that if 0 > 1, the student group cannot achieve the eradication of bears.
Expert Solution
Step 1

Given that,

C(y,x)=x-yxc(z)dz

Where x is the number of existing bears before removals, and y is the number of removals such that 0yx

The function c(z) is a sort of unit cost function, which is simply specified as c(z)=x-θ,  θ>0 and θ1

We have to find the total cost of eradication of bears that is  y=x as a function of x and θ

After that shows that if θ>1, the student group can not achieve the eradication of bears.

 

 

 

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