Suppose that in a biological system there are n species of animals and m sources of food.Let ï¿ represent the population of the jth species, for each j = 1, . . ., N;let bi represent the available daily supply of the ith food;and let aÿj represent the amount of the ith food consumed on average by a member of the jth species. The linear systema11x1 + a12X2 ++ A1n xnb₁,a21x1 + a22x2 ++ A2n xn: b2,am1x1 + am 2x2 +represents an equilibriumA. Let A = [aij]-==⠀: bm+ Amn Xnwhere there is a daily supply of food to precisely meet the average daily consumption of each species.=12 0 3="1 0 2 2 X = (xj) = [1000, 500, 350, 400], and b0 0 1 1(bį) = [3500, 2700, 900].Is there sufficient food to satisfy the average daily consumption?(Hint: The linear system holds if Axb. We don't exactly need this, but think about how the entries in Ax should be compared to those of b.)B. What is the maximum number of animals of species 1 that could be added to the system with the supply of food still meeting the consumption?(i.e. How large can ₁ be?)-

A. By enerting the given matrices of A and X,and multiplyng A and X,we got b=[3200 2500 750].

Answered: Is there sufficient food to satisfy the…

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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