You have $95,000 you would like to invest in three different stocks: MarkyB Inc., JohnJohn Ltd., and Garretts Spaghetti House. You would like to invest no more than $17,000 in Garretts Spaghetti House, and you want the amount you invest in MarkyB Inc., to be at least the amount invested in JohnJohn Ltd. and Garretts Spaghetti House combined.
If MarkyB Inc. earns 17% annual interest, JohnJohn Ltd. earns 15% annual interest, and Garretts Spaghetti House earns 6% 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 earned?
You should invest $   into MarkyB Inc., $   into JohnJohn Ltd., and $   into Garretts Spaghetti House, which will give you give you maximum annual interest $   .

We are given the following details about the investment amounts and constraints:

- You have a total of $95,000 to invest.
- The investments will be in three stocks: MarkyB Inc., JohnJohn Ltd., and Garretts Spaghetti House.
- The amount invested in Garretts Spaghetti House must be no more than $17,000.
- The amount invested in MarkyB Inc. must be at least as much as the combined investments in JohnJohn Ltd. and Garretts Spaghetti House.
- The interest rates are:
  - 17% for MarkyB Inc.
  - 15% for JohnJohn Ltd.
  - 6% for Garretts Spaghetti House

Let:
- $ x_1 $ be the amount invested in MarkyB Inc.
- $ x_2 $ be the amount invested in JohnJohn Ltd.
- $ x_3 $ be the amount invested in Garretts Spaghetti House.

### Objective:
Maximize the total annual interest earned:
\[
\text{Total Interest} = 0.17x_1 + 0.15x_2 + 0.06x_3
\]

### Constraints:
1. The total investment must equal $95,000:
   \[
   x_1 + x_2 + x_3 = 95,000
   \]
2. The amount invested in Garretts Spaghetti House must be no more than $17,000:
   \[
   x_3 \leq 17,000
   \]
3. The amount invested in MarkyB Inc. must be at least as much as the combined investments in JohnJohn Ltd. and Garretts Spaghetti House:
   \[
   x_1 \geq x_2 + x_3
   \]

This is a linear programming problem, and we can solve it using a mathematical approach (like the simplex method or an optimization solver). Let's solve this problem to determine how much should be invested in each stock to maximize the interest.It seems like I can’t do more advanced data analysis right now. Please try again later. If you have any other questions or would like to discuss this further, feel free to ask!

Would you like to explore an alternative approach or look at similar problems while we resolve this?

Here are 5 related questions that might be of interest:
1. What is linear programming, and how is it used in investment optimization?
2. How does the Simplex Method work in solving optimization problems?
3. What are the key benefits of diversifying investments across different stocks?
4. How do different interest rates impact long-term investment returns?
5. What factors should you consider when deciding to invest in high-interest but high-risk stocks?

**Tip:** Always consider potential risks along with returns when making investment decisions, especially in stocks with varying interest rates.

You have $95,000 you would like to invest in three different stocks: MarkyB Inc., JohnJohn Ltd., and Garretts Spaghetti House. You would like to invest no more than $17,000 in Garretts Spaghetti House, and you want the amount you invest in MarkyB Inc., to be at least the amount invested in JohnJohn Ltd. and Garretts Spaghetti House combined. If MarkyB Inc. earns 17% annual interest, JohnJohn Ltd. earns 15% annual interest, and Garretts Spaghetti House earns 6% 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 earned?

Learn how to solve a linear programming problem involving a $95,000 investment across three stocks: MarkyB Inc., JohnJohn Ltd., and Garretts Spaghetti House. This problem covers optimization, interest maximization, and constraint handling using algebra and linear programming techniques. Suitable for advanced high school and college students.

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