## Step 1: Define the symbolic representation of the problem

Let's define the symbolic variables:
- $x_1$ represents the number of shampoo bottles
- $x_2$ represents the number of conditioner bottles

The objective function to maximize profit is: $5x_1 + 6x_2$

The constraints are:
- $x_1 \geq 50$ (at least 50 shampoo bottles)
- $x_2 \geq 30$ (at least 30 conditioner bottles)
- $3x_1 + 4x_2 \leq 300$ (total time available is 300 minutes)

## Step 2: Convert the problem into a Gurobi code

We will use the Gurobi library in Python to solve this linear programming problem.

## Step 3: Write down the symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'shampoo bottles'), ('x2', 'conditioner bottles')],
    'objective_function': '5*x1 + 6*x2',
    'constraints': ['x1 >= 50', 'x2 >= 30', '3*x1 + 4*x2 <= 300']
}
```

## Step 4: Implement the problem in Gurobi Python code

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=50, name="shampoo_bottles")  # at least 50 shampoo bottles
    x2 = model.addVar(lb=30, name="conditioner_bottles")  # at least 30 conditioner bottles

    # Define the objective function
    model.setObjective(5 * x1 + 6 * x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(3 * x1 + 4 * x2 <= 300, name="time_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of shampoo bottles: {x1.varValue}")
        print(f"Number of conditioner bottles: {x2.varValue}")
        print(f"Max profit: {5 * x1.varValue + 6 * x2.varValue}")
    else:
        print("No optimal solution found.")

solve_problem()
```