To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's denote:
- $x_1$ as the amount invested in the fertilizer company,
- $x_2$ as the amount invested in the pesticide company.

The objective is to maximize profit. Given that each dollar invested in a fertilizer company yields a $0.14 profit and each dollar invested in a pesticide company yields a $0.15 profit, the objective function can be written as:
\[ \text{Maximize:} \quad 0.14x_1 + 0.15x_2 \]

The constraints based on the problem description are:
1. Total investment should not exceed $5000: \( x_1 + x_2 \leq 5000 \)
2. At least 50% of the total investment should be in the fertilizer company: \( x_1 \geq 0.5(x_1 + x_2) \)
3. At least $1000 should be invested in the pesticide company: \( x_2 \geq 1000 \)

Symbolic representation:
```json
{
  'sym_variables': [('x1', 'amount invested in fertilizer company'), ('x2', 'amount invested in pesticide company')],
  'objective_function': '0.14*x1 + 0.15*x2',
  'constraints': ['x1 + x2 <= 5000', 'x1 >= 0.5*(x1 + x2)', 'x2 >= 1000']
}
```

To implement this optimization problem in Gurobi using Python, we will use the following code:

```python
from gurobipy import *

# Create a new model
m = Model("Investment_Optimization")

# Define variables
x1 = m.addVar(name="Fertilizer_Investment", lb=0)
x2 = m.addVar(name="Pesticide_Investment", lb=0)

# Set the objective function
m.setObjective(0.14*x1 + 0.15*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 5000, name="Total_Investment")
m.addConstr(x1 >= 0.5*(x1 + x2), name="Fertilizer_Percentage")
m.addConstr(x2 >= 1000, name="Pesticide_Minimum")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Amount invested in Fertilizer Company: {x1.x}")
    print(f"Amount invested in Pesticide Company: {x2.x}")
else:
    print("No optimal solution found.")

```