To determine the correct system of inequalities representing the scenario, let's break down the problem and find the relevant constraints based on the given conditions.
1. Stock Value Condition:
- The company wants to maintain a stock value of at least [tex]$6000.
- The stock value is represented by the expression \( x^2 - 2y \).
- To maintain a value of at least $[/tex]6000, this can be translated into the inequality:
[tex]\[
x^2 - 2y \geq 6000
\][/tex]
2. Purchases Condition:
- The company wants to keep the purchases below [tex]$2000.
- The purchases are modeled by the expression \( 2x + 5y \).
- To ensure the purchases are below $[/tex]2000, this can be translated into the inequality:
[tex]\[
2x + 5y < 2000
\][/tex]
Thus, the constraints are:
[tex]\[
\begin{aligned}
&1. \quad x^2 - 2y \geq 6000 \\
&2. \quad 2x + 5y < 2000
\end{aligned}
\][/tex]
Given these two inequalities, the correct system of inequalities that represents this scenario is:
[tex]\[
\begin{array}{l}
x^2 - 2y \geq 6000 \\
2x + 5y < 2000
\end{array}
\][/tex]
This matches the option:
[tex]\[
\begin{array}{l}
x^2 - 2y \geq 6000 \\
2x + 5y < 2000
\end{array}
\][/tex]
So the correct answer is:
[tex]\[
\begin{array}{l}
x^2-2 y \geq 6000 \\
2 x+5 y<2000
\end{array}
\][/tex]
