Suppose that in a biological system there are n species of animals and m sources of food. Let xj represent the population of the jth species, for each j = 1, · · · , n; bi represent the available daily supply of the ith food; and aij represent the amount of the ith food consumed on the average by a member of the jth species. The linear system

represents an equilibrium where there is a daily supply of food to precisely meet the average daily consumption of each species.
a. Let

x = (xj) = [1000, 500, 350, 400], and b = (bi) = [3500, 2700, 900]. Is there sufficient food to satisfy the average daily consumption?
b. What is the maximum number of animals of each species that could be individually added to the system with the supply of food still meeting the consumption?
c. If species 1 became extinct, how much of an individual increase of each of the remaining species could be supported?
d. If species 2 became extinct, how much of an individual increase of each of the remaining species could be supported?

Transcribed Image Text:

3 A=[aij]=1 1 0 2 : 2