To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints.

Let's define:
- $x_1$ as the amount of vanilla cake mix purchased (in kg),
- $x_2$ as the amount of chocolate cake mix purchased (in kg).

The objective is to minimize the total cost, which can be represented by the objective function: 
\[ \text{Minimize} \quad 10x_1 + 15x_2 \]

Given that vanilla cake mix contains 3% leavening agent and chocolate cake mix contains 2% leavening agent, and the final mixture needs at least 0.3 kg of leavening agent, we have the constraint:
\[ 0.03x_1 + 0.02x_2 \geq 0.3 \]

Additionally, since vanilla cake mix contains 55% flour and chocolate cake mix contains 43% flour, and the final mixture needs at least 10 kg of flour, we have another constraint:
\[ 0.55x_1 + 0.43x_2 \geq 10 \]

Both $x_1$ and $x_2$ should be non-negative since they represent quantities of cake mixes.

The symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'vanilla cake mix'), ('x2', 'chocolate cake mix')],
    'objective_function': '10*x1 + 15*x2',
    'constraints': ['0.03*x1 + 0.02*x2 >= 0.3', '0.55*x1 + 0.43*x2 >= 10', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, name="vanilla_cake_mix")
x2 = m.addVar(lb=0, name="chocolate_cake_mix")

# Set the objective function
m.setObjective(10*x1 + 15*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(0.03*x1 + 0.02*x2 >= 0.3, "leavening_agent_constraint")
m.addConstr(0.55*x1 + 0.43*x2 >= 10, "flour_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Vanilla cake mix: {x1.x} kg")
    print(f"Chocolate cake mix: {x2.x} kg")
    print(f"Total cost: ${m.objVal}")
else:
    print("No optimal solution found")
```