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make a linear programming graph from this question

Let's first extract the details from the problem and then formulate the linear programming model to create the graph.

### Problem Statement Summary:
- **Total investment available**: $20,000.
- **Investment options**: Fund F1 and Fund F2.
- **Constraints**:
  1. The total investment in F1 and F2 is no more than $20,000.
  2. The investment in F1 is no less than $1,000.
  3. The investment in F2 offers at least 5% more return than F1.
  4. The return rates are:
     - F1: 10%
     - F2: 12%

Let $ x $ be the amount invested in Fund F1, and $ y $ be the amount invested in Fund F2.

### Objective Function:
The objective is to **maximize the return** on the investment, which is given by:
\[ \text{Maximize } Z = 0.10x + 0.12y \]

### Constraints:
1. $ x + y \leq 20,000 $  (Total investment cannot exceed $20,000)
2. $ x \geq 1,000 $  (At least $1,000 must be invested in F1)
3. $ y \geq 1.05x $  (F2 must have at least 5% more return than F1)

### Non-negativity constraints:
\[ x \geq 0, \quad y \geq 0 \]

Now, I'll plot these constraints on a graph to identify the feasible region and determine the optimal solution visually. I'll create the graph for the given linear programming problem.

Learn how to create a linear programming graph for an investment optimization problem with constraints and objective functions. Explore a practical example where $20,000 is invested between Fund F1 and Fund F2 to maximize returns, subject to investment limits and return requirements.

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