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Let's analyze the problem step by step.

### Given Information:
- You have $38,000 to invest in two stocks: **Stock Boll** and **Stock Coff**.
- The buying limit on Stock Coff is **$14,100**.
- You want to spend at least **twice as much money on Stock Boll** compared to Stock Coff.
- Stock Boll earns **8% annual interest**, while Stock Coff earns **4% annual interest**.

### Goal:
Maximize the total annual interest, and figure out how much to invest in each stock.

### Approach:

Let:
- $ x $ = amount invested in Stock Coff.
- $ 2x $ = amount invested in Stock Boll (since you are investing at least twice as much in Boll as Coff).

Total available investment:
\[ x + 2x = 3x = 38,000 \]
So:
\[ x = \frac{38,000}{3} = 12,666.67 \]
Thus, you would invest:
- $ x = 12,666.67 $ in Stock Coff.
- $ 2x = 25,333.33 $ in Stock Boll.

Now, let's calculate the interest earned from each:
- Interest from Stock Boll at 8%:
  \[ \text{Interest from Boll} = 0.08 \times 25,333.33 = 2,026.67 \]
- Interest from Stock Coff at 4%:
  \[ \text{Interest from Coff} = 0.04 \times 12,666.67 = 506.67 \]

### Total Annual Interest:
\[
\text{Total Interest} = 2,026.67 + 506.67 = 2,533.34
\]

This would be the maximum interest you can earn with this strategy.

Would you like more details on this or have any other questions? Here are some additional questions you might find useful:

1. What happens if the interest rates of the two stocks change?
2. How would the solution change if the condition of spending twice as much on Stock Boll didn't apply?
3. Can you still maximize interest if you have no limit on how much to invest in Stock Coff?
4. What if the total amount to invest was different?
5. How can we adjust the solution if there is a penalty or fee for going over a certain investment threshold?

**Tip:** Always double-check the conditions in investment problems to ensure you're maximizing returns under all constraints!

You have $38,000 you would like to invest in two different stocks, Stock Boll and Stock Coff. The buying limit on Stock Coff is $14,100 and you want to spend at least two times as much money on Stock Boll as Stock Coff. If Stock Boll earns 8% annual interest and Stock Coff earns 4% annual interest, how much money (in dollars) should you invest in each stock to maximize your annual interest earned? What is the maximum annual interest (in dollars)?

Learn how to maximize the annual interest earned from an investment of $38,000 in two stocks, Stock Boll and Stock Coff, where Stock Boll earns 8% and Stock Coff earns 4%. The buying limit on Stock Coff is $14,100, and you must invest at least two times as much in Stock Boll. A step-by-step solution demonstrates how to calculate the maximum annual interest.

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