Answer
stocks $5000$ dollars, bonds $5000$ dollars.
Work Step by Step
Step 1. Assume that the amount invested in stocks is $x$ dollars, and in bonds is $y$ dollars.
Step 2. Based on the given conditions, we have
$\begin{cases} x+y\leq10,000\\y\geq3000\\x\geq2000\\y\geq x \end{cases}$
Step 3. The equation for the returns can be expressed as
$R=0.12x + 0.08y$
Step 4. To maximize the return, graph the inequalities as shown and we can identify the corners of the solution region as:
$(2000,3000), (3000,3000),(2000,8000), (5000,5000)$.
Step 5. Check the value of the corner points with the return equation. We have
$R_1=0.12(2000) + 0.08(3000)=480$; $R_2=0.12(3000) + 0.08(3000)=600$; $R_3=0.12(2000) + 0.08(8000)=880$; $R_4=0.12(5000) + 0.08(5000)=1000$;
Step 6. We conclude that the amount invested in stocks should be $5000$ dollars, and in bonds should be $5000$ dollars to maximize the return.
