## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and the objective function based on the given problem description.

## Step 2: Identify the variables and their corresponding symbolic representations
Let $x_0$ represent 'grams of fat', $x_1$ represent 'milligrams of iron', and $x_2$ represent 'milligrams of magnesium'.

## 3: Translate the objective function into algebraic terms using symbolic variables
The objective function to minimize is $7x_0^2 + 5x_0x_1 + 6x_0x_2 + 5x_1^2 + x_1x_2 + 5x_2^2 + 3x_0 + 5x_2$.

## 4: List the constraints in semi-algebraic form using symbolic variables
The constraints are:
1. $4x_0 \leq 228$
2. $22x_0 \leq 271$
3. $11x_1 \leq 228$
4. $26x_1 \leq 271$
5. $9x_2 \leq 228$
6. $2x_2 \leq 271$
7. $4x_0 + 9x_2 \geq 67$
8. $11x_1 + 9x_2 \geq 40$
9. $16x_0^2 + 121x_1^2 \geq 39$
10. $4x_0 + 11x_1 + 9x_2 \geq 39$
11. $22x_0 + 26x_1 \geq 54$
12. $22x_0 + 2x_2 \geq 70$
13. $22x_0 + 26x_1 + 2x_2 \geq 70$
14. $9x_0 - 5x_2 \geq 0$
15. $4x_0 + 11x_1 \leq 214$
16. $22x_0^2 + 2x_2^2 \leq 258$
17. $26x_1 + 2x_2 \leq 216$
18. $22x_0 + 26x_1 \leq 247$

## 5: Provide the symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'grams of fat'), ('x1', 'milligrams of iron'), ('x2', 'milligrams of magnesium')],
'objective_function': '7*x0^2 + 5*x0*x1 + 6*x0*x2 + 5*x1^2 + x1*x2 + 5*x2^2 + 3*x0 + 5*x2',
'constraints': [
'4*x0 <= 228',
'22*x0 <= 271',
'11*x1 <= 228',
'26*x1 <= 271',
'9*x2 <= 228',
'2*x2 <= 271',
'4*x0 + 9*x2 >= 67',
'11*x1 + 9*x2 >= 40',
'16*x0^2 + 121*x1^2 >= 39',
'4*x0 + 11*x1 + 9*x2 >= 39',
'22*x0 + 26*x1 >= 54',
'22*x0 + 2*x2 >= 70',
'22*x0 + 26*x1 + 2*x2 >= 70',
'9*x0 - 5*x2 >= 0',
'4*x0 + 11*x1 <= 214',
'22*x0^2 + 2*x2^2 <= 258',
'26*x1 + 2*x2 <= 216',
'22*x0 + 26*x1 <= 247'
]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x0")
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x2")

    # Objective function
    model.setObjective(7*x0**2 + 5*x0*x1 + 6*x0*x2 + 5*x1**2 + x1*x2 + 5*x2**2 + 3*x0 + 5*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4*x0 <= 228)
    model.addConstr(22*x0 <= 271)
    model.addConstr(11*x1 <= 228)
    model.addConstr(26*x1 <= 271)
    model.addConstr(9*x2 <= 228)
    model.addConstr(2*x2 <= 271)
    model.addConstr(4*x0 + 9*x2 >= 67)
    model.addConstr(11*x1 + 9*x2 >= 40)
    model.addConstr(16*x0**2 + 121*x1**2 >= 39)
    model.addConstr(4*x0 + 11*x1 + 9*x2 >= 39)
    model.addConstr(22*x0 + 26*x1 >= 54)
    model.addConstr(22*x0 + 2*x2 >= 70)
    model.addConstr(22*x0 + 26*x1 + 2*x2 >= 70)
    model.addConstr(9*x0 - 5*x2 >= 0)
    model.addConstr(4*x0 + 11*x1 <= 214)
    model.addConstr(22*x0**2 + 2*x2**2 <= 258)
    model.addConstr(26*x1 + 2*x2 <= 216)
    model.addConstr(22*x0 + 26*x1 <= 247)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print("x0:", x0.varValue)
        print("x1:", x1.varValue)
        print("x2:", x2.varValue)
        print("Objective:", model.objVal)
    else:
        print("No optimal solution found.")

optimize_problem()
```