Question

A forest is populated with two species of​ animals, A and B. The forest supplies two kinds of​ food, F1 and F2. For one​ year, each member of species A requires 1 unit of F1 and 0.5 units of F2. Each member of species B requires 0.2 units of F1 and 1 unit of F 2. The forest can normally supply 550 units of F1 and 1265 units of F2 per year. What is the maximum total number of animals the forest can​ support?

-The forest can support at most ____ animals?

Answer 1

Note that the two animals require x + 0.2y units of F1 per year and 0.5x + y units of F2 per year. Since the forest supplies at most 600 units of F1 and 525 units of F2 of year, then:

(1) x + 0.2y ≤ 550

(2) 0.5x + y ≤ 1265

Since we cannot have negative animals, we also have:

(3) x ≥ 0

(4) y ≥ 0.

We want to maximize the total number of animals, x + y. By graphing the region bounded by these equations, we see that the vertices of the region are:

(0, 0), (550,0), (330, 1100), and (0,1265).

Out of these four points, (330, 1100) maximizes x + y.

Therefore, at most 330+1100 = 1430 animals can be supported by the forest.