## Problem Description and Symbolic Representation

The problem requires finding the optimal mix of two supplement drinks, orange flavored and apple flavored, to minimize cost while meeting the daily recommended intake of fiber and iron.

### Symbolic Representation

Let's define the symbolic variables:

* `x1`: orange flavored drink (servings)
* `x2`: apple flavored drink (servings)

The objective function is to minimize the total cost:

* `8x1 + 5x2`

The constraints are:

* Fiber intake: `4x1 + 6x2 >= 13`
* Iron intake: `5x1 + 3x2 >= 13`
* Non-negativity: `x1 >= 0, x2 >= 0`

### Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'orange flavored drink'), ('x2', 'apple flavored drink')],
    'objective_function': '8x1 + 5x2',
    'constraints': ['4x1 + 6x2 >= 13', '5x1 + 3x2 >= 13', 'x1 >= 0', 'x2 >= 0']
}
```

## Gurobi Code

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="orange_flavored_drink", lb=0)  # orange flavored drink (servings)
x2 = model.addVar(name="apple_flavored_drink", lb=0)  # apple flavored drink (servings)

# Define the objective function
model.setObjective(8 * x1 + 5 * x2, gp.GRB.MINIMIZE)

# Define the constraints
model.addConstr(4 * x1 + 6 * x2 >= 13, name="fiber_intake")  # fiber intake
model.addConstr(5 * x1 + 3 * x2 >= 13, name="iron_intake")  # iron intake

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Orange flavored drink: {x1.varValue} servings")
    print(f"Apple flavored drink: {x2.varValue} servings")
    print(f"Total cost: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```