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Answer :
To solve the problem, we need to model the company's goals using a system of inequalities. Here's how we can do this step-by-step:
1. Understanding the Stock Value Expression:
- The company's stock value is expressed as [tex]\(x^2 - 2y\)[/tex].
- The company wants this value to be at least [tex]$7,000.
- This condition can be written as the inequality: \(x^2 - 2y \geq 7000\).
2. Understanding the Purchases Expression:
- The company's purchases are represented by \(2x + 5y\).
- The goal is to keep these purchases below $[/tex]1,000.
- This condition can be expressed as: [tex]\(2x + 5y < 1000\)[/tex].
So, combining these two conditions, we create a system of inequalities that represents the scenario:
- First inequality: [tex]\(x^2 - 2y \geq 7000\)[/tex] (which ensures the stock value is at least [tex]$7,000).
- Second inequality: \(2x + 5y < 1000\) (which ensures the purchases remain below $[/tex]1,000).
This system of inequalities accurately models the company's goals as described in the problem.
1. Understanding the Stock Value Expression:
- The company's stock value is expressed as [tex]\(x^2 - 2y\)[/tex].
- The company wants this value to be at least [tex]$7,000.
- This condition can be written as the inequality: \(x^2 - 2y \geq 7000\).
2. Understanding the Purchases Expression:
- The company's purchases are represented by \(2x + 5y\).
- The goal is to keep these purchases below $[/tex]1,000.
- This condition can be expressed as: [tex]\(2x + 5y < 1000\)[/tex].
So, combining these two conditions, we create a system of inequalities that represents the scenario:
- First inequality: [tex]\(x^2 - 2y \geq 7000\)[/tex] (which ensures the stock value is at least [tex]$7,000).
- Second inequality: \(2x + 5y < 1000\) (which ensures the purchases remain below $[/tex]1,000).
This system of inequalities accurately models the company's goals as described in the problem.
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