## Problem Description and Symbolic Representation

The problem requires finding the minimum cost for a weight loss program that includes a minimum of 200 units of protein and 50 units of carbs. There are two cuisine options available: Indian and Thai. One plate of Indian food contains 13 units of protein and 23 units of carbs. One plate of Thai food contains 8 units of protein and 12 units of carbs. Indian food costs $12 per plate, and Thai food costs $15 per plate.

### Symbolic Representation

Let's define the symbolic variables:
- $x_1$ = number of plates of Indian food
- $x_2$ = number of plates of Thai food

The objective function to minimize is the total cost:
- $12x_1 + 15x_2$

The constraints are:
- Protein requirement: $13x_1 + 8x_2 \geq 200$
- Carb requirement: $23x_1 + 12x_2 \geq 50$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'plates of Indian food'), ('x2', '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'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Weight Loss Program")

# Define the variables
x1 = model.addVar(name="Indian_food", lb=0)  # plates of Indian food
x2 = model.addVar(name="Thai_food", lb=0)   # plates of Thai food

# Define the objective function
model.setObjective(12 * x1 + 15 * x2, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(13 * x1 + 8 * x2 >= 200, name="protein_requirement")
model.addConstr(23 * x1 + 12 * x2 >= 50, name="carb_requirement")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal cost: ${model.objVal:.2f}")
    print(f"Plates of Indian food: {x1.varValue:.2f}")
    print(f"Plates of Thai food: {x2.varValue:.2f}")
else:
    print("No optimal solution found.")
```