## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin B1', 'grams of fat', 'milligrams of vitamin B5'], which can be represented symbolically as 'x1', 'x2', and 'x3' respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- 'x1' for 'milligrams of vitamin B1'
- 'x2' for 'grams of fat'
- 'x3' for 'milligrams of vitamin B5'

## Step 3: Render the objective function with symbolic variables
The objective function to maximize is:
\[ 5.95x_1^2 + 6.36x_1x_2 + 6.77x_1x_3 + 6.34x_2^2 + 3.22x_2x_3 + 8.3x_3^2 + 5.13x_2 + 5.06x_3 \]

## 4: List the semi-algebraic constraints with symbolic variables
The constraints are:
- \( 8x_1 \leq 109 \)
- \( 11x_1 \leq 62 \)
- \( 2x_1 \leq 67 \)
- \( 1x_2 \leq 109 \)
- \( 3x_2 \leq 62 \)
- \( 1x_2 \leq 67 \)
- \( 2x_3 \leq 109 \)
- \( 8x_3 \leq 62 \)
- \( 3x_3 \leq 67 \)
- \( 8x_1 + 1x_2 \geq 36 \)
- \( 8x_1 + 2x_3 \geq 30 \)
- \( 8x_1 + 1x_2 + 2x_3 \geq 20 \)
- \( 11x_1 + 8x_3 \geq 12 \)
- \( 2x_1 + 1x_2 \geq 9 \)
- \( 2x_1 + 3x_3 \geq 19 \)
- \( 1x_2 + 3x_3 \geq 17 \)
- \( 2x_1 + 1x_2 + 3x_3 \geq 13 \)
- \( 8x_1 + 2x_3 \leq 42 \)
- \( 8^2x_1^2 + 1^2x_2^2 \leq 102 \)
- \( 8x_1 + 1x_2 + 2x_3 \leq 102 \)
- \( 3^2x_2^2 + 8^2x_3^2 \leq 31 \)
- \( 11x_1 + 8x_3 \leq 25 \)
- \( 11x_1 + 3x_2 + 8x_3 \leq 25 \)
- \( 2^2x_1^2 + 3^2x_3^2 \leq 46 \)
- \( 2x_1 + 1x_2 \leq 63 \)
- \( 2x_1 + 1x_2 + 3x_3 \leq 63 \)

## 5: Specify the variable types
- 'x1' (milligrams of vitamin B1) is continuous.
- 'x2' (grams of fat) is integer.
- 'x3' (milligrams of vitamin B5) is continuous.

## 6: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x1 = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1")  # milligrams of vitamin B1
x2 = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, vtype=gurobi.GRB.INTEGER, name="x2")  # grams of fat
x3 = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x3")  # milligrams of vitamin B5

# Objective function
m.setObjective(5.95*x1**2 + 6.36*x1*x2 + 6.77*x1*x3 + 6.34*x2**2 + 3.22*x2*x3 + 8.3*x3**2 + 5.13*x2 + 5.06*x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(8*x1 <= 109)
m.addConstr(11*x1 <= 62)
m.addConstr(2*x1 <= 67)
m.addConstr(1*x2 <= 109)
m.addConstr(3*x2 <= 62)
m.addConstr(1*x2 <= 67)
m.addConstr(2*x3 <= 109)
m.addConstr(8*x3 <= 62)
m.addConstr(3*x3 <= 67)
m.addConstr(8*x1 + 1*x2 >= 36)
m.addConstr(8*x1 + 2*x3 >= 30)
m.addConstr(8*x1 + 1*x2 + 2*x3 >= 20)
m.addConstr(11*x1 + 8*x3 >= 12)
m.addConstr(2*x1 + 1*x2 >= 9)
m.addConstr(2*x1 + 3*x3 >= 19)
m.addConstr(1*x2 + 3*x3 >= 17)
m.addConstr(2*x1 + 1*x2 + 3*x3 >= 13)
m.addConstr(8*x1 + 2*x3 <= 42)
m.addConstr(8**2*x1**2 + 1**2*x2**2 <= 102)
m.addConstr(8*x1 + 1*x2 + 2*x3 <= 102)
m.addConstr(3**2*x2**2 + 8**2*x3**2 <= 31)
m.addConstr(11*x1 + 8*x3 <= 25)
m.addConstr(11*x1 + 3*x2 + 8*x3 <= 25)
m.addConstr(2**2*x1**2 + 3**2*x3**2 <= 46)
m.addConstr(2*x1 + 1*x2 <= 63)
m.addConstr(2*x1 + 1*x2 + 3*x3 <= 63)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin B1'), 
        ('x2', 'grams of fat'), 
        ('x3', 'milligrams of vitamin B5')
    ], 
    'objective_function': '5.95*x1^2 + 6.36*x1*x2 + 6.77*x1*x3 + 6.34*x2^2 + 3.22*x2*x3 + 8.3*x3^2 + 5.13*x2 + 5.06*x3', 
    'constraints': [
        '8*x1 <= 109', 
        '11*x1 <= 62', 
        '2*x1 <= 67', 
        '1*x2 <= 109', 
        '3*x2 <= 62', 
        '1*x2 <= 67', 
        '2*x3 <= 109', 
        '8*x3 <= 62', 
        '3*x3 <= 67', 
        '8*x1 + 1*x2 >= 36', 
        '8*x1 + 2*x3 >= 30', 
        '8*x1 + 1*x2 + 2*x3 >= 20', 
        '11*x1 + 8*x3 >= 12', 
        '2*x1 + 1*x2 >= 9', 
        '2*x1 + 3*x3 >= 19', 
        '1*x2 + 3*x3 >= 17', 
        '2*x1 + 1*x2 + 3*x3 >= 13', 
        '8*x1 + 2*x3 <= 42', 
        '64*x1^2 + 1*x2^2 <= 102', 
        '8*x1 + 1*x2 + 2*x3 <= 102', 
        '9*x2^2 + 64*x3^2 <= 31', 
        '11*x1 + 8*x3 <= 25', 
        '11*x1 + 3*x2 + 8*x3 <= 25', 
        '4*x1^2 + 9*x3^2 <= 46', 
        '2*x1 + 1*x2 <= 63', 
        '2*x1 + 1*x2 + 3*x3 <= 63'
    ]
}
```