Let's break down the problem from question 10 and solve it step by step:

Problem Overview:

You have $94,000 to invest in three different stocks:

• MarkyB Inc. with 17% annual interest,
• JohnJohn Ltd. with 14% annual interest,
• Garretts Spaghetti House with 7% annual interest.

Constraints:

1. The amount you invest in MarkyB Inc. should be at least the amount you invest in JohnJohn Ltd. and Garretts Spaghetti House combined.
2. You can invest no more than $11,000 in Garretts Spaghetti House.

We need to determine how much to invest in each stock to maximize your total annual interest.

Define Variables:

• Let $x$ be the amount invested in MarkyB Inc..
• Let $y$ be the amount invested in JohnJohn Ltd..
• Let $z$ be the amount invested in Garretts Spaghetti House.

Constraints in Equation Form:

1. Total investment: $x + y + z = 94,000$
2. The amount invested in MarkyB Inc. should be at least the sum of the amounts invested in JohnJohn Ltd. and Garretts Spaghetti House: $x \geq y + z$
3. You cannot invest more than $11,000 in Garretts Spaghetti House: $z \leq 11,000$

Objective:

Maximize the annual interest earned, which can be written as: $\text{Interest} = 0.17x + 0.14y + 0.07z$

Solution Strategy:

We can set up and solve this system to maximize the interest while satisfying the constraints.

Let me calculate this for you.To maximize the total annual interest, you should invest the following amounts:

• MarkyB Inc.: $47,000
• JohnJohn Ltd.: $47,000
• Garretts Spaghetti House: $0

With these investments, the maximum annual interest you can earn is $14,570.

Would you like any further details on the process? Here are five related questions that expand on the topic:

1. What happens if you invest less in MarkyB Inc. and more in Garretts Spaghetti House?
2. How would the solution change if the interest rates were different for the stocks?
3. Can you explain how the constraint $x \geq y + z$ affects the investment strategy?
4. How does maximizing the interest depend on the upper limit of $11,000 for Garretts Spaghetti House?
5. Would removing the investment cap on Garretts Spaghetti House increase the annual interest?

Tip: In optimization problems, always pay attention to constraints and ensure they are strictly followed to get the best possible solution.