Suppose you have [tex]$\$[/tex] 16,000[tex]$ to invest in three stocks, A, B, and C. Stock A is a low-risk stock that has expected returns of $[/tex]4\%[tex]$. Stock B is a medium-risk stock that has expected returns of $[/tex]5\%[tex]$. Stock C is a high-risk stock that has expected returns of $[/tex]6\%[tex]$. You want to invest at least $[/tex]\[tex]$ 1,000$[/tex] in each stock. To balance the risks, you decide to invest no more than [tex]$\$[/tex] 7,000$ in stock C and to limit the amount invested in C to less than 4 times the amount invested in stock A. You also decide to invest less than twice as much in stock B as in stock A. How much should you invest in each stock to maximize your expected profit? Complete the constraints.

[tex]\[
\begin{array}{l}
\text{Stock A: } x \geq 1000 \\
\text{Stock B: } y \geq 1000 \\
\text{Stock C: } 16 - x - y \geq 1000 \\
16 - x - y \leq 7000 \\
16 - x - y \ \textless \ 4x \\
y \ \textless \ 2x \\
x + y + z = 16000
\end{array}
\][/tex]