## Problem Description and Symbolic Representation

The problem requires finding the minimum cost diet that meets the nutritional requirements of workers. The diet consists of soup and sandwiches.

### Symbolic Representation

Let's define the symbolic variables:
- $x_1$ = number of cans of soup
- $x_2$ = number of sandwiches

The objective is to minimize the total cost: $1x_1 + 3x_2$

The constraints are:
- Calories: $200x_1 + 250x_2 \geq 2000$
- Protein: $5x_1 + 10x_2 \geq 100$
- Carbs: $4x_1 + 15x_2 \geq 100$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'cans of soup'), ('x2', 'sandwiches')],
    'objective_function': '1*x1 + 3*x2',
    'constraints': [
        '200*x1 + 250*x2 >= 2000',
        '5*x1 + 10*x2 >= 100',
        '4*x1 + 15*x2 >= 100',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("diet_problem")

# Define variables
x1 = model.addVar(name="soup", lb=0)  # cans of soup
x2 = model.addVar(name="sandwich", lb=0)  # sandwiches

# Objective function: minimize total cost
model.setObjective(1*x1 + 3*x2, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(200*x1 + 250*x2 >= 2000, name="calories")
model.addConstr(5*x1 + 10*x2 >= 100, name="protein")
model.addConstr(4*x1 + 15*x2 >= 100, name="carbs")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Minimum cost: ${model.objVal:.2f}")
else:
    print("No optimal solution found")
```