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Harvesting of Animal Population, Uniform harvesting, Let X^0 denote the…

- - - - product with L matrix came out column vector modeling future population after single growth period. x(t+1)=Lx(t)
        
        will come out eigenvalue, λ that satisfied equation Lx(t)=λx(t)
        
        per usual λ calculate through det(L-λI)=0
        
        ans calculated
        
        0 < λ < 1 the population decreases to zero
        
        λ = 1 , the population approach a stable steady state
        
        λ > 1 , population growth boundlessly (Model Population Growth)
  - - - diagonal harvest matrix donated by the capital H
        
        vector containing number of females harvested from the each class.
        
        age distribution at the beginning of he next growth period : [ Lx(t) - HLx(t) = x(t) ]
- - - - Reduce to :
        
        R > 1 is the population increasing
  - - - In order to determine the optimal sustainable yield requires linear programming theory
  - - - Reduce:
        
        1/(1 − h) must be the unique positive eigenvalue λ1 of the Leslie growth matrix L
        
        Solve:
        
        The vector x1, in this case, is the same as the eigenvector of L corresponding to the eigenvalue λ1
        
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