MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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# MATH 1324 Written Assignment 2

## Section 4.6: Model and Solve Systems of Linear Equations Using Matrix Inverse Methods

### Problem Statement

Solve the following application using matrix inverse methods.

An international mining company has two mines in Voisey's Bay and Hawk Ridge. The composition of the ore from each field is given in the table:

| Mine          | Nickel (%) | Copper (%) |
|---------------|------------|------------|
| Voisey's Bay  | 2          | 4          |
| Hawk Ridge    | 3          | 2          |

How many tons of ore from each mine should be used to obtain each order of nickel and copper in the table below:

| Metal    | Order 1 | Order 2 |
|----------|---------|---------|
| Nickel   | 6 tons  | 8 tons  |
| Copper   | 8 tons  | 8 tons  |

### Solution

#### Step 1: Set Up the System of Equations

We can set up the linear system based on the given percentage compositions and required amounts:

For Nickel (N): 
\[ 2x_1 + 3x_2 = \text{Nickel amount} \]

For Copper (C):
\[ 4x_1 + 2x_2 = \text{Copper amount} \]

Here,
- \( x_1 \) = amount of ore from Voisey's Bay 
- \( x_2 \) = amount of ore from Hawk Ridge 

#### Step 2: Turn the System into Matrix Form

Using the given orders,
- For order 1:
  \[
  \begin{bmatrix}
  2 & 3 \\
  4 & 2 
  \end{bmatrix}
  \begin{bmatrix}
  x_1 \\
  x_2 
  \end{bmatrix} 
  =
  \begin{bmatrix}
  6 \\
  8 
  \end{bmatrix}
  \]

- For order 2:
  \[
  \begin{bmatrix}
  2 & 3 \\
  4 & 2 
  \end{bmatrix}
  \begin{bmatrix}
  x_1 \\
  x_2 
  \end{bmatrix} 
  =
  \begin{bmatrix}
  8
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Transcribed Image Text:# MATH 1324 Written Assignment 2 ## Section 4.6: Model and Solve Systems of Linear Equations Using Matrix Inverse Methods ### Problem Statement Solve the following application using matrix inverse methods. An international mining company has two mines in Voisey's Bay and Hawk Ridge. The composition of the ore from each field is given in the table: | Mine | Nickel (%) | Copper (%) | |---------------|------------|------------| | Voisey's Bay | 2 | 4 | | Hawk Ridge | 3 | 2 | How many tons of ore from each mine should be used to obtain each order of nickel and copper in the table below: | Metal | Order 1 | Order 2 | |----------|---------|---------| | Nickel | 6 tons | 8 tons | | Copper | 8 tons | 8 tons | ### Solution #### Step 1: Set Up the System of Equations We can set up the linear system based on the given percentage compositions and required amounts: For Nickel (N): \[ 2x_1 + 3x_2 = \text{Nickel amount} \] For Copper (C): \[ 4x_1 + 2x_2 = \text{Copper amount} \] Here, - \( x_1 \) = amount of ore from Voisey's Bay - \( x_2 \) = amount of ore from Hawk Ridge #### Step 2: Turn the System into Matrix Form Using the given orders, - For order 1: \[ \begin{bmatrix} 2 & 3 \\ 4 & 2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 6 \\ 8 \end{bmatrix} \] - For order 2: \[ \begin{bmatrix} 2 & 3 \\ 4 & 2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 8
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