## Step 1: Define the symbolic variables and their corresponding natural language objects.
The symbolic variables are defined as follows: 
- $x_0$ represents 'milligrams of zinc'
- $x_1$ represents 'grams of protein'
- $x_2$ represents 'milligrams of vitamin K'

## Step 2: Translate the objective function into an algebraic term using the symbolic variables.
The objective function to maximize is: $2.24x_0x_1 + 1.49x_0x_2 + 6.98x_2^2 + 8.11x_0 + 4.52x_1 + 9.76x_2$

## 3: List the semi-algebraic constraints using the symbolic variables.
The constraints are:
- $9x_0 \leq 218$
- $8x_0 \leq 93$
- $3x_0 \leq 175$
- $10x_0 \leq 140$
- $13x_1 \leq 218$
- $11x_1 \leq 93$
- $7x_1 \leq 175$
- $8x_1 \leq 140$
- $3x_2 \leq 218$
- $1x_2 \leq 93$
- $4x_2 \leq 175$
- $3x_2 \leq 140$
- $9x_0 + 3x_2 \geq 55$
- $8^2x_0^2 + 1^2x_2^2 \geq 20$
- $8x_0 + 11x_1 \geq 20$
- $3x_0 + 7x_1 \geq 33$
- $10x_0 + 8x_1 \geq 31$
- $9^2x_0^2 + 13^2x_1^2 \leq 151$
- $9x_0 + 3x_2 \leq 110$
- $13x_1 + 3x_2 \leq 162$
- $9x_0 + 13x_1 + 3x_2 \leq 162$
- $8^2x_0^2 + 11^2x_1^2 \leq 66$
- $11x_1 + 1x_2 \leq 65$
- $8x_0 + 1x_2 \leq 59$
- $8x_0 + 11x_1 + 1x_2 \leq 59$
- $3^2x_0^2 + 4^2x_2^2 \leq 83$
- $7x_1 + 4x_2 \leq 149$
- $3x_0 + 7x_1 + 4x_2 \leq 149$
- $10^2x_0^2 + 3^2x_2^2 \leq 69$
- $8x_1 + 3x_2 \leq 91$
- $10x_0 + 8x_1 + 3x_2 \leq 91$

## 4: Provide the symbolic representation of the problem.
```json
{
    'sym_variables': [
        ('x0', 'milligrams of zinc'), 
        ('x1', 'grams of protein'), 
        ('x2', 'milligrams of vitamin K')
    ], 
    'objective_function': '2.24*x0*x1 + 1.49*x0*x2 + 6.98*x2^2 + 8.11*x0 + 4.52*x1 + 9.76*x2', 
    'constraints': [
        '9*x0 <= 218',
        '8*x0 <= 93',
        '3*x0 <= 175',
        '10*x0 <= 140',
        '13*x1 <= 218',
        '11*x1 <= 93',
        '7*x1 <= 175',
        '8*x1 <= 140',
        '3*x2 <= 218',
        '1*x2 <= 93',
        '4*x2 <= 175',
        '3*x2 <= 140',
        '9*x0 + 3*x2 >= 55',
        '64*x0^2 + x2^2 >= 20',
        '8*x0 + 11*x1 >= 20',
        '3*x0 + 7*x1 >= 33',
        '10*x0 + 8*x1 >= 31',
        '81*x0^2 + 169*x1^2 <= 151',
        '9*x0 + 3*x2 <= 110',
        '13*x1 + 3*x2 <= 162',
        '9*x0 + 13*x1 + 3*x2 <= 162',
        '64*x0^2 + 121*x1^2 <= 66',
        '11*x1 + x2 <= 65',
        '8*x0 + x2 <= 59',
        '8*x0 + 11*x1 + x2 <= 59',
        '9*x0^2 + 16*x2^2 <= 83',
        '7*x1 + 4*x2 <= 149',
        '3*x0 + 7*x1 + 4*x2 <= 149',
        '100*x0^2 + 9*x2^2 <= 69',
        '8*x1 + 3*x2 <= 91',
        '10*x0 + 8*x1 + 3*x2 <= 91'
    ]
}
```

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

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="milligrams_of_zinc", lb=-float('inf'), ub=float('inf'))
x1 = m.addVar(name="grams_of_protein", lb=-float('inf'), ub=float('inf'))
x2 = m.addVar(name="milligrams_of_vitamin_K", lb=-float('inf'), ub=float('inf'))

# Objective function
m.setObjective(2.24*x0*x1 + 1.49*x0*x2 + 6.98*x2**2 + 8.11*x0 + 4.52*x1 + 9.76*x2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(9*x0 <= 218)
m.addConstr(8*x0 <= 93)
m.addConstr(3*x0 <= 175)
m.addConstr(10*x0 <= 140)
m.addConstr(13*x1 <= 218)
m.addConstr(11*x1 <= 93)
m.addConstr(7*x1 <= 175)
m.addConstr(8*x1 <= 140)
m.addConstr(3*x2 <= 218)
m.addConstr(x2 <= 93)
m.addConstr(4*x2 <= 175)
m.addConstr(3*x2 <= 140)
m.addConstr(9*x0 + 3*x2 >= 55)
m.addConstr(64*x0**2 + x2**2 >= 20)
m.addConstr(8*x0 + 11*x1 >= 20)
m.addConstr(3*x0 + 7*x1 >= 33)
m.addConstr(10*x0 + 8*x1 >= 31)
m.addConstr(81*x0**2 + 169*x1**2 <= 151)
m.addConstr(9*x0 + 3*x2 <= 110)
m.addConstr(13*x1 + 3*x2 <= 162)
m.addConstr(9*x0 + 13*x1 + 3*x2 <= 162)
m.addConstr(64*x0**2 + 121*x1**2 <= 66)
m.addConstr(11*x1 + x2 <= 65)
m.addConstr(8*x0 + x2 <= 59)
m.addConstr(8*x0 + 11*x1 + x2 <= 59)
m.addConstr(9*x0**2 + 16*x2**2 <= 83)
m.addConstr(7*x1 + 4*x2 <= 149)
m.addConstr(3*x0 + 7*x1 + 4*x2 <= 149)
m.addConstr(100*x0**2 + 9*x2**2 <= 69)
m.addConstr(8*x1 + 3*x2 <= 91)
m.addConstr(10*x0 + 8*x1 + 3*x2 <= 91)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.Status.OPTIMAL:
    print("Optimal solution found.")
    print(f"Milligrams of zinc: {x0.varValue}")
    print(f"Grams of protein: {x1.varValue}")
    print(f"Milligrams of vitamin K: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```