To solve this problem, we need to represent the company's goals using a system of inequalities.
1. For the company's stock value goal:
- It is stated that the company wants to maintain a stock value of at least [tex]$7,000.
- The expression for stock value is \( x^2 - 2y \).
- "At least $[/tex]7,000" means the stock value should be greater than or equal to [tex]$7,000.
- This can be written as an inequality: \( x^2 - 2y \geq 7000 \).
2. For the company's purchase constraint:
- The company wants to keep purchases below $[/tex]1,000.
- The expression for purchases is [tex]\( 2x + 5y \)[/tex].
- "Below [tex]$1,000" means the purchases should be less than $[/tex]1,000.
- This can be written as an inequality: [tex]\( 2x + 5y < 1000 \)[/tex].
Putting both inequalities together, we get the system of inequalities that represents the scenario:
[tex]\[
\begin{array}{r}
x^2 - 2y \geq 7000 \\
2x + 5y < 1000
\end{array}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\begin{array}{r}
x^2 - 2y \geq 7000 \\
2x + 5y < 1000
\end{array}
\][/tex]
