## Step 1: Define the symbolic representation of the problem
Let's denote the amount invested in the logging industry as $x_1$ and the amount invested in the shipping industry as $x_2$. The problem description can be translated into a symbolic representation as follows:

- Variables: 
  - $x_1$ represents the amount invested in the logging industry.
  - $x_2$ represents the amount invested in the shipping industry.

## Step 2: Formulate the objective function
The objective is to maximize profit. Each dollar invested in the logging industry yields a $0.06 profit, and each dollar invested in the shipping industry yields a $0.03 profit. Therefore, the objective function can be written as:
\[ \text{Maximize:} \quad 0.06x_1 + 0.03x_2 \]

## 3: Define the constraints
1. Total investment constraint: Jacob has $3000 to invest.
\[ x_1 + x_2 \leq 3000 \]
2. Minimum logging industry investment constraint: A minimum of 50% of the money has to be invested in the logging industry.
\[ x_1 \geq 0.5(x_1 + x_2) \]
Simplifying, we get:
\[ x_1 \geq 0.5x_1 + 0.5x_2 \]
\[ 0.5x_1 \geq 0.5x_2 \]
\[ x_1 \geq x_2 \]
3. Minimum shipping industry investment constraint: At least $1000 has to be invested in the shipping industry.
\[ x_2 \geq 1000 \]
4. Non-negativity constraints: Investments cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## 4: Symbolic representation in JSON format
```json
{
'sym_variables': [('x1', 'logging industry investment'), ('x2', 'shipping industry investment')],
'objective_function': '0.06*x1 + 0.03*x2',
'constraints': [
    'x1 + x2 <= 3000',
    'x1 >= x2',
    'x2 >= 1000',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 5: Gurobi code in Python
```python
import gurobi

def solve_investment_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="logging_investment", lb=0)
    x2 = model.addVar(name="shipping_investment", lb=0)

    # Objective function: Maximize 0.06*x1 + 0.03*x2
    model.setObjective(0.06 * x1 + 0.03 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 3000, name="total_investment")
    model.addConstr(x1 >= x2, name="logging_min_percentage")
    model.addConstr(x2 >= 1000, name="shipping_min_investment")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal investment in logging industry: $", x1.varValue)
        print("Optimal investment in shipping industry: $", x2.varValue)
        print("Maximum profit: $", 0.06 * x1.varValue + 0.03 * x2.varValue)
    else:
        print("The problem is infeasible")

solve_investment_problem()
```