Problema Solution
A privately owned lake contains two types of fish: bass and trout. The
owner provides two types of food, A and B, for these fish. Trout require 4
units of food A and 5 units of food B, and bass require 10 units of food A
and 4 units of food B. If the owner has 1600 units of food A and 1000 units
of food B, find the maximum number of fish that the lake can support.
Answer provided by our tutors
Let
x = the number of bass, x>=0
y = the number of trout, y>=0
4x + 10y <= 1600
5x + 4y <= 1000
The number of fish is F(x, y) = x + y is the objective function.
First we find the corner points:
The corner points are: (200, 0), (0, 160), (106, 118).
The we calculate F(x, y) at each of the corner points:
F(200, 0) = 200 + 0 = 200
F(0, 160) = 0 + 160 = 160
F(106, 118) = 106 + 118 = 224
The maximum number of fish is 224.