## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are:
- $x_0$: milligrams of vitamin K
- $x_1$: milligrams of vitamin B9
- $x_2$: milligrams of vitamin B3
- $x_3$: milligrams of vitamin D

The objective function to minimize is:
\[ 4x_0^2 + 6x_0x_1 + x_0x_2 + 8x_0x_3 + x_1^2 + 8x_1x_2 + 7x_1x_3 + 6x_2x_3 + 8x_3^2 + 5x_1 + 7x_2 + 4x_3 \]

## Step 2: List the constraints
The constraints given are:
1. $17x_0 \leq 478$
2. $15x_0 \leq 413$
3. $5x_1 \leq 478$
4. $18x_1 \leq 413$
5. $4x_2 \leq 478$
6. $29x_2 \leq 413$
7. $3x_3 \leq 478$
8. $24x_3 \leq 413$
9. $4x_2 + 3x_3 \geq 96$
10. $17x_0 + 5x_1 \geq 91$
11. $17^2x_0^2 + 3^2x_3^2 \geq 105$
12. $5x_1 + 4x_2 \geq 116$
13. $17x_0 + 5x_1 + 4x_2 + 3x_3 \geq 116$
14. $15^2x_0^2 + 24^2x_3^2 \geq 90$
15. $29^2x_2^2 + 24^2x_3^2 \geq 45$
16. $18^2x_1^2 + 29^2x_2^2 \geq 38$
17. $15^2x_0^2 + 18^2x_1^2 + 29^2x_2^2 \geq 75$
18. $15x_0 + 18x_1 + 29x_2 + 24x_3 \geq 75$
19. $-2x_0 + 9x_2 \geq 0$
20. $6x_1 - 5x_2 \geq 0$
21. $5x_1^2 + 4x_2^2 + 3x_3^2 \leq 282$
22. $17x_0 + 5x_1 + 4x_2 \leq 325$
23. $17^2x_0^2 + 4^2x_2^2 + 3^2x_3^2 \leq 172$
24. $18x_1 + 24x_3 \leq 130$
25. $29x_2 + 24x_3 \leq 412$
26. $15^2x_0^2 + 29^2x_2^2 \leq 183$
27. $15x_0 + 24x_3 \leq 258$
28. $18x_1 + 29x_2 + 24x_3 \leq 164$
29. $15^2x_0^2 + 18^2x_1^2 + 24^2x_3^2 \leq 128$
30. $15x_0 + 18x_1 + 29x_2 \leq 226$

## Step 3: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin K'),
        ('x1', 'milligrams of vitamin B9'),
        ('x2', 'milligrams of vitamin B3'),
        ('x3', 'milligrams of vitamin D')
    ],
    'objective_function': '4*x0^2 + 6*x0*x1 + x0*x2 + 8*x0*x3 + x1^2 + 8*x1*x2 + 7*x1*x3 + 6*x2*x3 + 8*x3^2 + 5*x1 + 7*x2 + 4*x3',
    'constraints': [
        '17*x0 <= 478',
        '15*x0 <= 413',
        '5*x1 <= 478',
        '18*x1 <= 413',
        '4*x2 <= 478',
        '29*x2 <= 413',
        '3*x3 <= 478',
        '24*x3 <= 413',
        '4*x2 + 3*x3 >= 96',
        '17*x0 + 5*x1 >= 91',
        '289*x0^2 + 9*x3^2 >= 105',
        '5*x1 + 4*x2 >= 116',
        '17*x0 + 5*x1 + 4*x2 + 3*x3 >= 116',
        '225*x0^2 + 576*x3^2 >= 90',
        '841*x2^2 + 576*x3^2 >= 45',
        '324*x1^2 + 841*x2^2 >= 38',
        '225*x0^2 + 324*x1^2 + 841*x2^2 >= 75',
        '15*x0 + 18*x1 + 29*x2 + 24*x3 >= 75',
        '-2*x0 + 9*x2 >= 0',
        '6*x1 - 5*x2 >= 0',
        '25*x1^2 + 16*x2^2 + 9*x3^2 <= 282',
        '17*x0 + 5*x1 + 4*x2 <= 325',
        '289*x0^2 + 16*x2^2 + 9*x3^2 <= 172',
        '18*x1 + 24*x3 <= 130',
        '29*x2 + 24*x3 <= 412',
        '225*x0^2 + 841*x2^2 <= 183',
        '15*x0 + 24*x3 <= 258',
        '18*x1 + 29*x2 + 24*x3 <= 164',
        '225*x0^2 + 324*x1^2 + 576*x3^2 <= 128',
        '15*x0 + 18*x1 + 29*x2 <= 226'
    ]
}
```

## 4: Gurobi Code
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # milligrams of vitamin K
    x1 = model.addVar(name="x1", lb=0)  # milligrams of vitamin B9
    x2 = model.addVar(name="x2", lb=0, integrality=1)  # milligrams of vitamin B3
    x3 = model.addVar(name="x3", lb=0)  # milligrams of vitamin D

    # Objective function
    model.setObjective(4*x0**2 + 6*x0*x1 + x0*x2 + 8*x0*x3 + x1**2 + 8*x1*x2 + 7*x1*x3 + 6*x2*x3 + 8*x3**2 + 5*x1 + 7*x2 + 4*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(17*x0 <= 478)
    model.addConstr(15*x0 <= 413)
    model.addConstr(5*x1 <= 478)
    model.addConstr(18*x1 <= 413)
    model.addConstr(4*x2 <= 478)
    model.addConstr(29*x2 <= 413)
    model.addConstr(3*x3 <= 478)
    model.addConstr(24*x3 <= 413)
    model.addConstr(4*x2 + 3*x3 >= 96)
    model.addConstr(17*x0 + 5*x1 >= 91)
    model.addConstr(289*x0**2 + 9*x3**2 >= 105)
    model.addConstr(5*x1 + 4*x2 >= 116)
    model.addConstr(17*x0 + 5*x1 + 4*x2 + 3*x3 >= 116)
    model.addConstr(225*x0**2 + 576*x3**2 >= 90)
    model.addConstr(841*x2**2 + 576*x3**2 >= 45)
    model.addConstr(324*x1**2 + 841*x2**2 >= 38)
    model.addConstr(225*x0**2 + 324*x1**2 + 841*x2**2 >= 75)
    model.addConstr(15*x0 + 18*x1 + 29*x2 + 24*x3 >= 75)
    model.addConstr(-2*x0 + 9*x2 >= 0)
    model.addConstr(6*x1 - 5*x2 >= 0)
    model.addConstr(25*x1**2 + 16*x2**2 + 9*x3**2 <= 282)
    model.addConstr(17*x0 + 5*x1 + 4*x2 <= 325)
    model.addConstr(289*x0**2 + 16*x2**2 + 9*x3**2 <= 172)
    model.addConstr(18*x1 + 24*x3 <= 130)
    model.addConstr(29*x2 + 24*x3 <= 412)
    model.addConstr(225*x0**2 + 841*x2**2 <= 183)
    model.addConstr(15*x0 + 24*x3 <= 258)
    model.addConstr(18*x1 + 29*x2 + 24*x3 <= 164)
    model.addConstr(225*x0**2 + 324*x1**2 + 576*x3**2 <= 128)
    model.addConstr(15*x0 + 18*x1 + 29*x2 <= 226)

    model.optimize()

    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print("Objective: ", model.objVal)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
    else:
        print("No optimal solution found.")

optimize_problem()
```