## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'green beans' and 'hamburgers', which we can represent symbolically as $x_1$ and $x_2$ respectively. The objective function to minimize is $8.4x_1 + 6.91x_2$. The constraints are:
1. $5x_1 + 4x_2 \geq 10$ (at least 10 milligrams of calcium from both),
2. $5x_1 \geq 10$ (at least 10 milligrams of calcium from green beans),
3. $4x_2 \geq 10$ (at least 10 milligrams of calcium from hamburgers, but note this seems to be incorrectly stated as it should be about the total or a direct condition on $x_2$),
4. $x_1 - x_2 \geq 0$ (one times the number of green beans, plus -1 times the number of hamburgers has to be no less than zero),
5. $5x_1 + 4x_2 \leq 21$ (up to 21 milligrams of calcium from both),
6. $0 \leq x_1$ and $0 \leq x_2$ are implicitly considered since fractional numbers are allowed and there's no direct upper bound given other than the calcium constraints.

## 2: Correct and Clarify Constraints
Upon review, it seems there might have been a misunderstanding in the direct translation of constraints, especially regarding the source of calcium. The constraints should reflect:
- $5x_1 + 4x_2 \geq 10$ (total calcium),
- The individual constraints might have been misstated, but essentially we have:
  - $x_1 \geq 2$ (from $5x_1 \geq 10$),
  - $x_2 \geq 2.5$ (from $4x_2 \geq 10$),
- $x_1 - x_2 \geq 0$,
- $5x_1 + 4x_2 \leq 21$.

## 3: Symbolic Representation
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'green beans'), ('x2', 'hamburgers')],
'objective_function': '8.4*x1 + 6.91*x2',
'constraints': [
    '5*x1 + 4*x2 >= 10',
    '5*x1 >= 10',
    '4*x2 >= 10',
    'x1 - x2 >= 0',
    '5*x1 + 4*x2 <= 21'
]
}
```

## 4: Gurobi Code
Now, let's implement this in Gurobi:
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    green_beans = model.addVar(lb=0, name="green_beans", vtype=gurobi.GRB.CONTINUOUS)
    hamburgers = model.addVar(lb=0, name="hamburgers", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(8.4 * green_beans + 6.91 * hamburgers, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5 * green_beans + 4 * hamburgers >= 10, name="total_calcium")
    model.addConstr(5 * green_beans >= 10, name="green_beans_calcium")
    model.addConstr(4 * hamburgers >= 10, name="hamburgers_calcium")
    model.addConstr(green_beans - hamburgers >= 0, name="balance")
    model.addConstr(5 * green_beans + 4 * hamburgers <= 21, name="calcium_limit")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Green beans: {green_beans.varValue}")
        print(f"Hamburgers: {hamburgers.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```