## Step 1: Define the symbolic representation of the variables
The variables are ['grams of fat', 'milligrams of vitamin E', 'milligrams of vitamin B1', 'milligrams of vitamin A', 'milligrams of vitamin C']. Let's denote them as $x_1, x_2, x_3, x_4, x_5$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is:
$1.83x_1^2 + 8.56x_1x_2 + 7.73x_1x_3 + 3.94x_1x_4 + 7.98x_1x_5 + 4.15x_2^2 + 1.78x_2x_3 + 2.28x_2x_4 + 7.57x_2x_5 + 3.2x_3^2 + 4.42x_3x_4 + 7.06x_3x_5 + 4.1x_4^2 + 8.39x_4x_5 + 6.68x_5^2 + 6.82x_1 + 8.6x_2 + 3.58x_3 + 6.45x_4 + 2.31x_5$

## 3: List the constraints
Constraints:
1. $4x_1 \leq 391$
2. $11x_1 \leq 483$
3. $20x_2 \leq 391$
4. $20x_2 \leq 483$
5. $26x_3 \leq 391$
6. $7x_3 \leq 483$
7. $25x_4 \leq 391$
8. $29x_4 \leq 483$
9. $22x_5 \leq 391$
10. $11x_5 \leq 483$
11. $26x_3^2 + 22x_5^2 \geq 29$
12. $4x_1^2 + 25x_4^2 \geq 28$
13. $4x_1 + 20x_2 \geq 51$
14. $4x_1^2 + 20x_2^2 + 25x_4^2 \geq 39$
15. $20x_2 + 26x_3 + 25x_4 \geq 39$
16. $4x_1 + 20x_2 + 26x_3 \geq 39$
17. $20x_2 + 26x_3 + 22x_5 \geq 39$
18. $4x_1^2 + 20x_2^2 + 25x_4^2 \geq 76$
19. $20x_2 + 26x_3 + 25x_4 \geq 76$
20. $4x_1 + 20x_2 + 26x_3 \geq 76$
21. $20x_2 + 26x_3 + 22x_5 \geq 76$
22. $4x_1 + 20x_2 + 25x_4 \geq 53$
23. $20x_2 + 26x_3 + 25x_4 \geq 53$
24. $4x_1 + 20x_2 + 26x_3 \geq 53$
25. $20x_2 + 26x_3 + 22x_5 \geq 53$
26. $4x_1 + 20x_2 + 25x_4 \geq 47$
27. $20x_2 + 26x_3 + 25x_4 \geq 47$
28. $4x_1^2 + 20x_2^2 + 26x_3^2 \geq 47$
29. $20x_2 + 26x_3 + 22x_5 \geq 47$
30. $26x_3^2 + 25x_4^2 \leq 324$
31. $20x_2 + 22x_5 \leq 162$
32. $4x_1 + 20x_2 \leq 322$
33. $4x_1^2 + 26x_3^2 \leq 244$
34. $4x_1 + 20x_2 + 26x_3 + 25x_4 + 22x_5 \leq 244$
35. $29x_4 + 11x_5 \leq 240$
36. $20x_2 + 29x_4 \leq 122$
37. $11x_1 + 20x_2 + 7x_3 + 29x_4 + 11x_5 \leq 122$
38. $x_1 \in \mathbb{Z}$
39. $x_2 \in \mathbb{Z}$
40. $x_3 \in \mathbb{R}$
41. $x_4 \in \mathbb{R}$
42. $x_5 \in \mathbb{R}$

## Step 4: Write the Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # grams of fat
x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin E
x3 = model.addVar(name="x3", vtype=gurobi.GRB.CONTINUOUS)  # milligrams of vitamin B1
x4 = model.addVar(name="x4", vtype=gurobi.GRB.CONTINUOUS)  # milligrams of vitamin A
x5 = model.addVar(name="x5", vtype=gurobi.GRB.CONTINUOUS)  # milligrams of vitamin C

# Define the objective function
model.setObjective(1.83*x1**2 + 8.56*x1*x2 + 7.73*x1*x3 + 3.94*x1*x4 + 7.98*x1*x5 + 
                   4.15*x2**2 + 1.78*x2*x3 + 2.28*x2*x4 + 7.57*x2*x5 + 3.2*x3**2 + 
                   4.42*x3*x4 + 7.06*x3*x5 + 4.1*x4**2 + 8.39*x4*x5 + 6.68*x5**2 + 
                   6.82*x1 + 8.6*x2 + 3.58*x3 + 6.45*x4 + 2.31*x5, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(4 * x1 <= 391)
model.addConstr(11 * x1 <= 483)
model.addConstr(20 * x2 <= 391)
model.addConstr(20 * x2 <= 483)
model.addConstr(26 * x3 <= 391)
model.addConstr(7 * x3 <= 483)
model.addConstr(25 * x4 <= 391)
model.addConstr(29 * x4 <= 483)
model.addConstr(22 * x5 <= 391)
model.addConstr(11 * x5 <= 483)
model.addConstr(26 * x3**2 + 22 * x5**2 >= 29)
model.addConstr(4 * x1**2 + 25 * x4**2 >= 28)
model.addConstr(4 * x1 + 20 * x2 >= 51)
model.addConstr(4 * x1**2 + 20 * x2**2 + 25 * x4**2 >= 39)
model.addConstr(20 * x2 + 26 * x3 + 25 * x4 >= 39)
model.addConstr(4 * x1 + 20 * x2 + 26 * x3 >= 39)
model.addConstr(20 * x2 + 26 * x3 + 22 * x5 >= 39)
model.addConstr(4 * x1**2 + 20 * x2**2 + 25 * x4**2 >= 76)
model.addConstr(20 * x2 + 26 * x3 + 25 * x4 >= 76)
model.addConstr(4 * x1 + 20 * x2 + 26 * x3 >= 76)
model.addConstr(20 * x2 + 26 * x3 + 22 * x5 >= 76)
model.addConstr(4 * x1 + 20 * x2 + 25 * x4 >= 53)
model.addConstr(20 * x2 + 26 * x3 + 25 * x4 >= 53)
model.addConstr(4 * x1 + 20 * x2 + 26 * x3 >= 53)
model.addConstr(20 * x2 + 26 * x3 + 22 * x5 >= 53)
model.addConstr(4 * x1 + 20 * x2 + 25 * x4 >= 47)
model.addConstr(20 * x2 + 26 * x3 + 25 * x4 >= 47)
model.addConstr(4 * x1**2 + 20 * x2**2 + 26 * x3**2 >= 47)
model.addConstr(20 * x2 + 26 * x3 + 22 * x5 >= 47)
model.addConstr(26 * x3**2 + 25 * x4**2 <= 324)
model.addConstr(20 * x2 + 22 * x5 <= 162)
model.addConstr(4 * x1 + 20 * x2 <= 322)
model.addConstr(4 * x1**2 + 26 * x3**2 <= 244)
model.addConstr(4 * x1 + 20 * x2 + 26 * x3 + 25 * x4 + 22 * x5 <= 244)
model.addConstr(29 * x4 + 11 * x5 <= 240)
model.addConstr(20 * x2 + 29 * x4 <= 122)
model.addConstr(11 * x1 + 20 * x2 + 7 * x3 + 29 * x4 + 11 * x5 <= 122)

# Solve the model
model.optimize()

# Print the solution
print("Objective: ", model.objVal)
print("x1: ", x1.varValue)
print("x2: ", x2.varValue)
print("x3: ", x3.varValue)
print("x4: ", x4.varValue)
print("x5: ", x5.varValue)
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'grams of fat'), 
        ('x2', 'milligrams of vitamin E'), 
        ('x3', 'milligrams of vitamin B1'), 
        ('x4', 'milligrams of vitamin A'), 
        ('x5', 'milligrams of vitamin C')
    ], 
    'objective_function': '1.83*x1^2 + 8.56*x1*x2 + 7.73*x1*x3 + 3.94*x1*x4 + 7.98*x1*x5 + 4.15*x2^2 + 1.78*x2*x3 + 2.28*x2*x4 + 7.57*x2*x5 + 3.2*x3^2 + 4.42*x3*x4 + 7.06*x3*x5 + 4.1*x4^2 + 8.39*x4*x5 + 6.68*x5^2 + 6.82*x1 + 8.6*x2 + 3.58*x3 + 6.45*x4 + 2.31*x5', 
    'constraints': [
        '4*x1 <= 391', 
        '11*x1 <= 483', 
        '20*x2 <= 391', 
        '20*x2 <= 483', 
        '26*x3 <= 391', 
        '7*x3 <= 483', 
        '25*x4 <= 391', 
        '29*x4 <= 483', 
        '22*x5 <= 391', 
        '11*x5 <= 483', 
        '26*x3^2 + 22*x5^2 >= 29', 
        '4*x1^2 + 25*x4^2 >= 28', 
        '4*x1 + 20*x2 >= 51', 
        '4*x1^2 + 20*x2^2 + 25*x4^2 >= 39', 
        '20*x2 + 26*x3 + 25*x4 >= 39', 
        '4*x1 + 20*x2 + 26*x3 >= 39', 
        '20*x2 + 26*x3 + 22*x5 >= 39', 
        '4*x1^2 + 20*x2^2 + 25*x4^2 >= 76', 
        '20*x2 + 26*x3 + 25*x4 >= 76', 
        '4*x1 + 20*x2 + 26*x3 >= 76', 
        '20*x2 + 26*x3 + 22*x5 >= 76', 
        '4*x1 + 20*x2 + 25*x4 >= 53', 
        '20*x2 + 26*x3 + 25*x4 >= 53', 
        '4*x1 + 20*x2 + 26*x3 >= 53', 
        '20*x2 + 26*x3 + 22*x5 >= 53', 
        '4*x1 + 20*x2 + 25*x4 >= 47', 
        '20*x2 + 26*x3 + 25*x4 >= 47', 
        '4*x1^2 + 20*x2^2 + 26*x3^2 >= 47', 
        '20*x2 + 26*x3 + 22*x5 >= 47', 
        '26*x3^2 + 25*x4^2 <= 324', 
        '20*x2 + 22*x5 <= 162', 
        '4*x1 + 20*x2 <= 322', 
        '4*x1^2 + 26*x3^2 <= 244', 
        '4*x1 + 20*x2 + 26*x3 + 25*x4 + 22*x5 <= 244', 
        '29*x4 + 11*x5 <= 240', 
        '20*x2 + 29*x4 <= 122', 
        '11*x1 + 20*x2 + 7*x3 + 29*x4 + 11*x5 <= 122'
    ]
}
```