Three different bacteria are cultured in one environment and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third nutrient. Each individual of species II consumes 2 units of the first nutrient and 2 units of the third nutrient. Each individual of species III consumes 2 units of the first nutrient, 3 units of the second nutrient, and 5 units of the third nutrient. The culture is given 5,300 units of the first nutrient, 6,000 units of the second nutrient, and 11,300 units of the third nutrient. Let x = individuals of species I, y = individuals of species II, and z = individuals of species III.Write an equation for the total number of units of the first nutrient in terms of x, y, and z. Write an equation for the total number of units of the second nutrient in terms of x, y, and z. Write an equation for the total number of units of the third nutrient in terms of x, y, and z. How many of each species can be supported such that all of the nutrients are consumed? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.)(x, y, z) = , where 700 ≤ z ≤ 2000

Arrange the given information in a table and use the table to obtain a system of equations.

Three different bacteria are cultured in one environment and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third nutrient. Each individual of species II consumes 2 units of the first nutrient and 2 units of the third nutrient. Each individual of species III consumes 2 units of the first nutrient, 3 units of the second nutrient, and 5 units of the third nutrient. The culture is given 5,300 units of the first nutrient, 6,000 units of the second

Three different bacteria are cultured in one environment and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third nutrient. Each individual of species II consumes 2 units of the first nutrient and 2 units of the third nutrient. Each individual of species III consumes 2 units of the first nutrient, 3 units of the second nutrient, and 5 units of the third nutrient. The culture is given 5,300 units of the first nutrient, 6,000 units of the second

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Question

x = individuals of species I,

y = individuals of species II,

and

z = individuals of species III.

Write an equation for the total number of units of the first nutrient in terms of x, y, and z.

Write an equation for the total number of units of the second nutrient in terms of x, y, and z.

Write an equation for the total number of units of the third nutrient in terms of x, y, and z.

How many of each species can be supported such that all of the nutrients are consumed? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.)

(x, y, z) =

, where 700 ≤ z ≤ 2000

Expert Solution