## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, and then list the constraints.

### Variables
- $x_1$ represents the number of rubber ducks.
- $x_2$ represents the number of toy boats.

### Objective Function
The profit per rubber duck is $2, and the profit per toy boat is $4. The objective is to maximize profit, so the objective function is:
\[ \text{Maximize:} \quad 2x_1 + 4x_2 \]

### Constraints
1. Preparation time constraint: Each rubber duck takes 5 minutes, and each toy boat takes 8 minutes. There are 1000 minutes available for preparation.
\[ 5x_1 + 8x_2 \leq 1000 \]
2. Testing time constraint: Each rubber duck takes 3 minutes, and each toy boat takes 2 minutes. There are 700 minutes available for testing.
\[ 3x_1 + 2x_2 \leq 700 \]
3. Non-negativity constraint: The number of rubber ducks and toy boats cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'rubber ducks'), ('x2', 'toy boats')],
    'objective_function': '2*x1 + 4*x2',
    'constraints': [
        '5*x1 + 8*x2 <= 1000',
        '3*x1 + 2*x2 <= 700',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="rubber_ducks", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="toy_boats", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Maximize 2*x1 + 4*x2
    model.setObjective(2*x1 + 4*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(5*x1 + 8*x2 <= 1000, name="preparation_time")
    model.addConstr(3*x1 + 2*x2 <= 700, name="testing_time")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("The model is infeasible")

solve_optimization_problem()
```