Happy Quack pet food is made from corn, seeds, and beans. Each pound of corn provides 10 units of fiber, 10 units of fat, and 10 units of protein. Each pound of seeds provides 10 units of fiber, 20 units of fat, and 20 units of protein. Each pound of beans provides 10 units of fiber, 20 units of fat, and 40 units of protein. How many pounds of each ingredient are needed to make a feed that supplies a total of 400 units of fiber, 600 units of fat, and 800 units of protein? Use G-J Elimination method. a) Write the system of equations. Define the variables.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Problem Statement

**1) Happy Quack pet food is made from corn, seeds, and beans.**  
Each pound of corn provides 10 units of fiber, 10 units of fat, and 10 units of protein. Each pound of seeds provides 10 units of fiber, 20 units of fat, and 20 units of protein. Each pound of beans provides 10 units of fiber, 20 units of fat, and 40 units of protein. How many pounds of each ingredient are needed to make a feed that supplies a total of 400 units of fiber, 600 units of fat, and 800 units of protein? **Use G-J Elimination method.**

### Instructions

**a) Write the system of equations. Define the variables.**

- Define variables to represent the number of pounds of corn, seeds, and beans. Then, create equations based on the nutritional content and required totals.

**b) Write the augmented matrix for this problem.**

- Formulate the augmented matrix by organizing the coefficients and constants from the system of equations.

**c) Solve using Gauss-Jordan elimination method. Label answers.**

- Apply the Gauss-Jordan elimination method to solve the system of equations represented by the augmented matrix. Clearly label the solutions, indicating how many pounds of each ingredient are needed.
Transcribed Image Text:### Problem Statement **1) Happy Quack pet food is made from corn, seeds, and beans.** Each pound of corn provides 10 units of fiber, 10 units of fat, and 10 units of protein. Each pound of seeds provides 10 units of fiber, 20 units of fat, and 20 units of protein. Each pound of beans provides 10 units of fiber, 20 units of fat, and 40 units of protein. How many pounds of each ingredient are needed to make a feed that supplies a total of 400 units of fiber, 600 units of fat, and 800 units of protein? **Use G-J Elimination method.** ### Instructions **a) Write the system of equations. Define the variables.** - Define variables to represent the number of pounds of corn, seeds, and beans. Then, create equations based on the nutritional content and required totals. **b) Write the augmented matrix for this problem.** - Formulate the augmented matrix by organizing the coefficients and constants from the system of equations. **c) Solve using Gauss-Jordan elimination method. Label answers.** - Apply the Gauss-Jordan elimination method to solve the system of equations represented by the augmented matrix. Clearly label the solutions, indicating how many pounds of each ingredient are needed.
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