## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of freight train trips.
- $x_2$ represents the number of cargo ship trips.

## Step 2: Formulate the objective function
The objective is to maximize the total number of fish transported. Given that freight trains can take 2000 fish per trip and cargo ships can take 7000 fish per trip, the objective function can be written as:
\[ \text{Maximize:} \quad 2000x_1 + 7000x_2 \]

## 3: Define the constraints
1. Budget constraint: The cost per trip for freight trains is $100 and for cargo ships is $180, with a budget of at most $1500.
\[ 100x_1 + 180x_2 \leq 1500 \]
2. Trip constraint: The number of freight train trips must be less than the number of cargo ship trips.
\[ x_1 < x_2 \]
3. Non-negativity constraint: The number of trips cannot be negative.
\[ x_1 \geq 0, \quad x_2 \geq 0 \]
4. Integer constraint: Since the number of trips must be an integer, $x_1$ and $x_2$ should be integers.

## 4: Convert to Gurobi code
To solve this linear programming problem using Gurobi, we will use Python. Note that Gurobi can handle integer constraints directly.

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="x1", lb=0, vtype=gurobi.GRB.INTEGER)  # Freight train trips
x2 = model.addVar(name="x2", lb=0, vtype=gurobi.GRB.INTEGER)  # Cargo ship trips

# Objective function: Maximize 2000x1 + 7000x2
model.setObjective(2000*x1 + 7000*x2, gurobi.GRB.MAXIMIZE)

# Budget constraint: 100x1 + 180x2 <= 1500
model.addConstr(100*x1 + 180*x2 <= 1500, name="budget_constraint")

# Trip constraint: x1 < x2
model.addConstr(x1 <= x2 - 1, name="trip_constraint")  # Adjusted for integer solution

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution:")
    print(f"Freight train trips: {x1.varValue}")
    print(f"Cargo ship trips: {x2.varValue}")
    print(f"Total fish transported: {2000*x1.varValue + 7000*x2.varValue}")
else:
    print("No optimal solution found.")
```

## 5: Symbolic Representation
The symbolic representation of the problem is as follows:
```json
{
    'sym_variables': [('x1', 'freight train trips'), ('x2', 'cargo ship trips')],
    'objective_function': '2000*x1 + 7000*x2',
    'constraints': [
        '100*x1 + 180*x2 <= 1500',
        'x1 < x2'
    ]
}
```

The final answer is: 
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="x1", lb=0, vtype=gurobi.GRB.INTEGER)  # Freight train trips
x2 = model.addVar(name="x2", lb=0, vtype=gurobi.GRB.INTEGER)  # Cargo ship trips

# Objective function: Maximize 2000x1 + 7000x2
model.setObjective(2000*x1 + 7000*x2, gurobi.GRB.MAXIMIZE)

# Budget constraint: 100x1 + 180x2 <= 1500
model.addConstr(100*x1 + 180*x2 <= 1500, name="budget_constraint")

# Trip constraint: x1 < x2
model.addConstr(x1 <= x2 - 1, name="trip_constraint")  # Adjusted for integer solution

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution:")
    print(f"Freight train trips: {x1.varValue}")
    print(f"Cargo ship trips: {x2.varValue}")
    print(f"Total fish transported: {2000*x1.varValue + 7000*x2.varValue}")
else:
    print("No optimal solution found.")
```