## Problem Description and Symbolic Representation

The problem requires finding the optimal mix of carrot juice and lemon juice to minimize cost while meeting the daily recommended intake of vitamin A and vitamin B.

### Symbolic Representation

Let's define the symbolic variables:

* `x1`: carrot juice
* `x2`: lemon juice

The objective function is to minimize the total cost:

* `3.5x1 + 6x2`

The constraints are:

* `8x1 + 3x2 >= 25` (minimum vitamin A intake)
* `3x1 + 6x2 >= 25` (minimum vitamin B intake)
* `x1, x2 >= 0` (non-negativity constraints)

### Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'carrot juice'), ('x2', 'lemon juice')],
    'objective_function': '3.5x1 + 6x2',
    'constraints': [
        '8x1 + 3x2 >= 25',
        '3x1 + 6x2 >= 25',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="carrot_juice", lb=0)
x2 = model.addVar(name="lemon_juice", lb=0)

# Define the objective function
model.setObjective(3.5 * x1 + 6 * x2, gp.GRB.MINIMIZE)

# Define the constraints
model.addConstr(8 * x1 + 3 * x2 >= 25, name="vitamin_A")
model.addConstr(3 * x1 + 6 * x2 >= 25, name="vitamin_B")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Carrot juice: {x1.varValue}")
    print(f"Lemon juice: {x2.varValue}")
    print(f"Total cost: {model.objVal}")
else:
    print("No optimal solution found.")
```