To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- $x_1$ as the number of plates of Indian food,
- $x_2$ as the number of plates of Thai food.

The objective is to minimize the total cost, which can be represented as $12x_1 + 15x_2$, since each plate of Indian food costs $12 and each plate of Thai food costs $15.

The constraints are:
1. The program must include a minimum of 200 units of protein: $13x_1 + 8x_2 \geq 200$.
2. The program must include a minimum of 50 units of carbs: $23x_1 + 12x_2 \geq 50$.
3. Non-negativity constraints, as the number of plates cannot be negative: $x_1 \geq 0$, $x_2 \geq 0$.

Therefore, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of plates of Indian food'), ('x2', 'number of plates of Thai food')],
    'objective_function': '12*x1 + 15*x2',
    'constraints': ['13*x1 + 8*x2 >= 200', '23*x1 + 12*x2 >= 50', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="IndianFood", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="ThaiFood", lb=0)

# Set the objective function
m.setObjective(12*x1 + 15*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(13*x1 + 8*x2 >= 200, "ProteinRequirement")
m.addConstr(23*x1 + 12*x2 >= 50, "CarbRequirement")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of plates of Indian food: {x1.x}")
    print(f"Number of plates of Thai food: {x2.x}")
    print(f"Minimum cost: ${m.objVal:.2f}")
else:
    print("No optimal solution found.")
```