## Step 1: Define the symbolic representation of the variables
The variables are 'grams of protein' and 'milligrams of vitamin K', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $3x_1^2 + 2x_1x_2 + 9x_2^2 + 5x_1 + 2x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $11x_1 \leq 58$ (energy stability index for grams of protein, but it's given as an equality in the problem statement, so $11x_1 = 58$ is not correct, instead we have $x_1 \geq 0$ and $x_1 \leq \infty$ but a specific value $x_0 = 11$ is given for $r_0$ which seems to imply $11 = 11x_1$ or $x_1 = 1$ for $r_0$),
- $4x_1 \leq 76$ (cardiovascular support index of grams of protein),
- $4x_1 \leq 59$ (digestive support index for grams of protein),
- $10x_2 \leq 58$ (energy stability index for milligrams of vitamin K),
- $4x_2 \leq 76$ (cardiovascular support index for milligrams of vitamin K),
- $7x_2 \leq 59$ (digestive support index for milligrams of vitamin K),
- $11^2x_1^2 + 10^2x_2^2 \geq 23^2$ (total combined energy stability index from grams of protein squared and milligrams of vitamin K squared),
- $11x_1 + 10x_2 \geq 23$ (total combined energy stability index from grams of protein and milligrams of vitamin K),
- $4^2x_1^2 + 4^2x_2^2 \geq 37^2$ (total combined cardiovascular support index from grams of protein squared and milligrams of vitamin K squared),
- $4x_1 + 4x_2 \geq 37$ (total combined cardiovascular support index from grams of protein and milligrams of vitamin K),
- $4^2x_1^2 + 7^2x_2^2 \geq 22^2$ (total combined digestive support index from grams of protein squared and milligrams of vitamin K squared, corrected to reflect the proper indices),
- $4x_1 + 7x_2 \geq 22$ (total combined digestive support index from grams of protein and milligrams of vitamin K),
- $5x_1^2 - 8x_2^2 \geq 0$,
- $11^2x_1^2 + 10^2x_2^2 \leq 55^2$ (total combined energy stability index from grams of protein squared and milligrams of vitamin K squared should be at maximum 55),
- $4x_1 + 4x_2 \leq 66$ (total combined cardiovascular support index from grams of protein and milligrams of vitamin K should be at maximum 66),
- $4^2x_1^2 + 7^2x_2^2 \leq 59^2$ (total combined digestive support index from grams of protein squared and milligrams of vitamin K squared should be no more than 59),
- $x_1 \in \mathbb{Z}$ (do not use a fractional amount of grams of protein),
- $x_2 \in \mathbb{R}$ (can have a fractional number of milligrams of vitamin K).

However, based on the problem description, we need to adjust our understanding of the constraints:
- The energy stability index for grams of protein is given as $r_0 = 11$ with $x_0 = 11$,
- The cardiovascular support index of grams of protein is $r_1 = 4$ with $x_0 = 4$,
- The digestive support index for grams of protein is $r_2 = 4$ with $x_0 = 4$,
- milligrams of vitamin K have an energy stability index of $10$,
- The cardiovascular support index for milligrams of vitamin K is $4$,
- The digestive support index for milligrams of vitamin K is $7$.

This implies:
- $x_1 = 1$ (from $11x_1 = 11$),
- And other constraints are directly given.

## 4: Correctly formulate the problem in Gurobi
Given the corrections and accurate formulation:
- Let $x_1$ be 'grams of protein' and $x_2$ be 'milligrams of vitamin K'.

## 5: Write down the problem in mathematical terms
Minimize $3x_1^2 + 2x_1x_2 + 9x_2^2 + 5x_1 + 2x_2$

Subject to:
- $x_1 = 1$ (from given condition, not directly a constraint but a fixed value),
- $5x_1^2 - 8x_2^2 \geq 0$,
- $121x_1^2 + 100x_2^2 \geq 529$,
- $11x_1 + 10x_2 \geq 23$,
- $16x_1^2 + 16x_2^2 \geq 1369$,
- $4x_1 + 4x_2 \geq 37$,
- $16x_1^2 + 49x_2^2 \geq 484$,
- $4x_1 + 7x_2 \geq 22$,
- $121x_1^2 + 100x_2^2 \leq 3025$,
- $4x_1 + 4x_2 \leq 66$,
- $16x_1^2 + 49x_2^2 \leq 3481$,
- $x_1 \in \mathbb{Z}$,
- $x_2 \in \mathbb{R}$.

## 6: Provide the symbolic representation
```json
{
    'sym_variables': [('x1', 'grams of protein'), ('x2', 'milligrams of vitamin K')],
    'objective_function': '3*x1^2 + 2*x1*x2 + 9*x2^2 + 5*x1 + 2*x2',
    'constraints': [
        'x1 = 1',
        '5*x1^2 - 8*x2^2 >= 0',
        '121*x1^2 + 100*x2^2 >= 529',
        '11*x1 + 10*x2 >= 23',
        '16*x1^2 + 16*x2^2 >= 1369',
        '4*x1 + 4*x2 >= 37',
        '16*x1^2 + 49*x2^2 >= 484',
        '4*x1 + 7*x2 >= 22',
        '121*x1^2 + 100*x2^2 <= 3025',
        '4*x1 + 4*x2 <= 66',
        '16*x1^2 + 49*x2^2 <= 3481',
        'x1 ∈ ℤ',
        'x2 ∈ ℝ'
    ]
}
```

## 7: Implement the problem in Gurobi
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(vtype=gurobi.GRB.INTEGER, name="x1") # grams of protein
    x2 = model.addVar(vtype=gurobi.GRB.CONTINUOUS, name="x2") # milligrams of vitamin K

    # Objective function
    model.setObjective(3*x1**2 + 2*x1*x2 + 9*x2**2 + 5*x1 + 2*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(x1 == 1, name="protein_constraint")
    model.addConstr(5*x1**2 - 8*x2**2 >= 0, name="stability_constraint")
    model.addConstr(121*x1**2 + 100*x2**2 >= 529, name="energy_stability_constraint")
    model.addConstr(11*x1 + 10*x2 >= 23, name="combined_energy_stability_constraint")
    model.addConstr(16*x1**2 + 16*x2**2 >= 1369, name="cardiovascular_support_constraint")
    model.addConstr(4*x1 + 4*x2 >= 37, name="combined_cardiovascular_support_constraint")
    model.addConstr(16*x1**2 + 49*x2**2 >= 484, name="digestive_support_constraint")
    model.addConstr(4*x1 + 7*x2 >= 22, name="combined_digestive_support_constraint")
    model.addConstr(121*x1**2 + 100*x2**2 <= 3025, name="max_energy_stability_constraint")
    model.addConstr(4*x1 + 4*x2 <= 66, name="max_cardiovascular_support_constraint")
    model.addConstr(16*x1**2 + 49*x2**2 <= 3481, name="max_digestive_support_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```