To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote the number of rubber ducks as $x_1$ and the number of toy boats as $x_2$. The profit per rubber duck is $2, and the profit per toy boat is $4. Each rubber duck takes 5 minutes of preparation and 3 minutes of testing to make, while each toy boat takes 8 minutes of preparation and 2 minutes of testing. The total available time for preparation is 1000 minutes, and for testing, it's 700 minutes.

The symbolic representation of the problem can be described as follows:

```json
{
    'sym_variables': [('x1', 'rubber ducks'), ('x2', 'toy boats')],
    'objective_function': '2*x1 + 4*x2',
    'constraints': [
        '5*x1 + 8*x2 <= 1000',  # Preparation time constraint
        '3*x1 + 2*x2 <= 700',   # Testing time constraint
        'x1 >= 0',               # Non-negativity constraint for rubber ducks
        'x2 >= 0'                # Non-negativity constraint for toy boats
    ]
}
```

This representation captures the essence of the problem: maximizing profit (`2*x1 + 4*x2`) under the constraints of limited preparation and testing time, with non-negativity constraints to ensure that we cannot produce a negative number of items.

To solve this linear programming problem using Gurobi in Python, we will use the following code:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="rubber_ducks")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="toy_boats")

# Set the objective function
m.setObjective(2*x1 + 4*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x1 + 8*x2 <= 1000, "preparation_time")
m.addConstr(3*x1 + 2*x2 <= 700, "testing_time")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Rubber Ducks: {x1.x}")
    print(f"Toy Boats: {x2.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```