## Step 1: Define the symbolic representation of the problem
The problem involves four variables: 'milligrams of vitamin B4', 'milligrams of vitamin B9', 'milligrams of vitamin D', and 'milligrams of vitamin C'. Let's denote these as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $5.18x_0 + 3.4x_1 + 4.47x_2 + 7.55x_3$.

## 3: List the constraints in symbolic notation
Constraints:
- $28x_0 \leq 436$
- $x_0 \leq 355$
- $15x_0 \leq 394$
- $7x_0 \leq 626$
- $13x_1 \leq 436$
- $24x_1 \leq 355$
- $12x_1 \leq 394$
- $8x_1 \leq 626$
- $4x_2 \leq 436$
- $x_2 \leq 355$
- $16x_2 \leq 394$
- $11x_2 \leq 626$
- $18x_3 \leq 436$
- $12x_3 \leq 355$
- $x_3 \leq 394$
- $13x_3 \leq 626$
- $13x_1 + 4x_2 \geq 36$
- $13x_1 + 18x_3 \geq 61$
- $28x_0 + 18x_3 \geq 91$
- $13x_1 + 4x_2 + 18x_3 \geq 96$
- $28x_0 + 13x_1 + 18x_3 \geq 96$
- $13x_1 + 4x_2 + 18x_3 \geq 99$
- $28x_0 + 13x_1 + 18x_3 \geq 99$
- $28x_0 + 13x_1 + 4x_2 + 18x_3 \geq 99$
- $x_0 + 12x_3 \geq 61$
- $x_2 + 12x_3 \geq 44$
- $24x_1 + x_2 \geq 86$
- $x_0 + 24x_1 + 12x_3 \geq 72$
- $x_0 + x_2 + 12x_3 \geq 72$
- $x_0 + 24x_1 + 12x_3 \geq 69$
- $x_0 + x_2 + 12x_3 \geq 69$
- $x_0 + x_1 + x_2 + 12x_3 \geq 69$
- $16x_2 + x_3 \geq 77$
- $12x_1 + 16x_2 \geq 38$
- $15x_0 + 16x_2 \geq 43$
- $12x_1 + x_3 \geq 91$
- $15x_0 + 12x_1 \geq 67$
- $15x_0 + x_3 \geq 94$
- $12x_1 + 16x_2 + x_3 \geq 96$
- $15x_0 + 12x_1 + 16x_2 \geq 96$
- $12x_1 + 16x_2 + x_3 \geq 76$
- $15x_0 + 12x_1 + 16x_2 \geq 76$
- $15x_0 + 12x_1 + 16x_2 + x_3 \geq 76$
- $8x_1 + 11x_2 \geq 146$
- $11x_2 + 13x_3 \geq 114$
- $7x_0 + 8x_1 \geq 140$
- $7x_0 + 13x_3 \geq 89$
- $7x_0 + 8x_1 + 11x_2 \geq 97$
- $8x_1 + 11x_2 + 13x_3 \geq 97$
- $7x_0 + 8x_1 + 13x_3 \geq 97$
- $7x_0 + 8x_1 + 11x_2 \geq 89$
- $8x_1 + 11x_2 + 13x_3 \geq 89$
- $7x_0 + 8x_1 + 13x_3 \geq 89$
- $7x_0 + 8x_1 + 11x_2 \geq 119$
- $8x_1 + 11x_2 + 13x_3 \geq 119$
- $7x_0 + 8x_1 + 13x_3 \geq 119$
- $7x_0 + 8x_1 + 11x_2 + 13x_3 \geq 119$
- $13x_1 + 18x_3 \leq 160$
- $13x_1 + 4x_2 \leq 251$
- $x_0 + 12x_3 \leq 94$
- $x_0 + 24x_1 + 12x_3 \leq 140$
- $15x_0 + 16x_2 + x_3 \leq 349$
- $7x_0 + 8x_1 + 11x_2 \leq 359$
- $8x_1 + 11x_2 + 13x_3 \leq 536$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin B4'),
        ('x1', 'milligrams of vitamin B9'),
        ('x2', 'milligrams of vitamin D'),
        ('x3', 'milligrams of vitamin C')
    ],
    'objective_function': '5.18*x0 + 3.4*x1 + 4.47*x2 + 7.55*x3',
    'constraints': [
        '28*x0 <= 436',
        'x0 <= 355',
        '15*x0 <= 394',
        '7*x0 <= 626',
        '13*x1 <= 436',
        '24*x1 <= 355',
        '12*x1 <= 394',
        '8*x1 <= 626',
        '4*x2 <= 436',
        'x2 <= 355',
        '16*x2 <= 394',
        '11*x2 <= 626',
        '18*x3 <= 436',
        '12*x3 <= 355',
        'x3 <= 394',
        '13*x3 <= 626',
        '13*x1 + 4*x2 >= 36',
        '13*x1 + 18*x3 >= 61',
        '28*x0 + 18*x3 >= 91',
        '13*x1 + 4*x2 + 18*x3 >= 96',
        '28*x0 + 13*x1 + 18*x3 >= 96',
        '13*x1 + 4*x2 + 18*x3 >= 99',
        '28*x0 + 13*x1 + 18*x3 >= 99',
        '28*x0 + 13*x1 + 4*x2 + 18*x3 >= 99',
        'x0 + 12*x3 >= 61',
        'x2 + 12*x3 >= 44',
        '24*x1 + x2 >= 86',
        'x0 + 24*x1 + 12*x3 >= 72',
        'x0 + x2 + 12*x3 >= 72',
        'x0 + 24*x1 + 12*x3 >= 69',
        'x0 + x2 + 12*x3 >= 69',
        'x0 + x1 + x2 + 12*x3 >= 69',
        '16*x2 + x3 >= 77',
        '12*x1 + 16*x2 >= 38',
        '15*x0 + 16*x2 >= 43',
        '12*x1 + x3 >= 91',
        '15*x0 + 12*x1 >= 67',
        '15*x0 + x3 >= 94',
        '12*x1 + 16*x2 + x3 >= 96',
        '15*x0 + 12*x1 + 16*x2 >= 96',
        '12*x1 + 16*x2 + x3 >= 76',
        '15*x0 + 12*x1 + 16*x2 >= 76',
        '15*x0 + 12*x1 + 16*x2 + x3 >= 76',
        '8*x1 + 11*x2 >= 146',
        '11*x2 + 13*x3 >= 114',
        '7*x0 + 8*x1 >= 140',
        '7*x0 + 13*x3 >= 89',
        '7*x0 + 8*x1 + 11*x2 >= 97',
        '8*x1 + 11*x2 + 13*x3 >= 97',
        '7*x0 + 8*x1 + 13*x3 >= 97',
        '7*x0 + 8*x1 + 11*x2 >= 89',
        '8*x1 + 11*x2 + 13*x3 >= 89',
        '7*x0 + 8*x1 + 13*x3 >= 89',
        '7*x0 + 8*x1 + 11*x2 >= 119',
        '8*x1 + 11*x2 + 13*x3 >= 119',
        '7*x0 + 8*x1 + 13*x3 >= 119',
        '7*x0 + 8*x1 + 11*x2 + 13*x3 >= 119',
        '13*x1 + 18*x3 <= 160',
        '13*x1 + 4*x2 <= 251',
        'x0 + 12*x3 <= 94',
        'x0 + 24*x1 + 12*x3 <= 140',
        '15*x0 + 16*x2 + x3 <= 349',
        '7*x0 + 8*x1 + 11*x2 <= 359',
        '8*x1 + 11*x2 + 13*x3 <= 536'
    ]
}
```

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

# Define the model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="x0", lb=-gp.GRB.INFINITY)  # milligrams of vitamin B4
x1 = m.addVar(name="x1", lb=-gp.GRB.INFINITY)  # milligrams of vitamin B9
x2 = m.addVar(name="x2", lb=-gp.GRB.INFINITY)  # milligrams of vitamin D
x3 = m.addVar(name="x3", lb=-gp.GRB.INFINITY)  # milligrams of vitamin C

# Define the objective function
m.setObjective(5.18*x0 + 3.4*x1 + 4.47*x2 + 7.55*x3, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(28*x0 <= 436)
m.addConstr(x0 <= 355)
m.addConstr(15*x0 <= 394)
m.addConstr(7*x0 <= 626)
m.addConstr(13*x1 <= 436)
m.addConstr(24*x1 <= 355)
m.addConstr(12*x1 <= 394)
m.addConstr(8*x1 <= 626)
m.addConstr(4*x2 <= 436)
m.addConstr(x2 <= 355)
m.addConstr(16*x2 <= 394)
m.addConstr(11*x2 <= 626)
m.addConstr(18*x3 <= 436)
m.addConstr(12*x3 <= 355)
m.addConstr(x3 <= 394)
m.addConstr(13*x3 <= 626)
m.addConstr(13*x1 + 4*x2 >= 36)
m.addConstr(13*x1 + 18*x3 >= 61)
m.addConstr(28*x0 + 18*x3 >= 91)
m.addConstr(13*x1 + 4*x2 + 18*x3 >= 96)
m.addConstr(28*x0 + 13*x1 + 18*x3 >= 96)
m.addConstr(13*x1 + 4*x2 + 18*x3 >= 99)
m.addConstr(28*x0 + 13*x1 + 18*x3 >= 99)
m.addConstr(28*x0 + 13*x1 + 4*x2 + 18*x3 >= 99)
m.addConstr(x0 + 12*x3 >= 61)
m.addConstr(x2 + 12*x3 >= 44)
m.addConstr(24*x1 + x2 >= 86)
m.addConstr(x0 + 24*x1 + 12*x3 >= 72)
m.addConstr(x0 + x2 + 12*x3 >= 72)
m.addConstr(x0 + 24*x1 + 12*x3 >= 69)
m.addConstr(x0 + x2 + 12*x3 >= 69)
m.addConstr(x0 + x1 + x2 + 12*x3 >= 69)
m.addConstr(16*x2 + x3 >= 77)
m.addConstr(12*x1 + 16*x2 >= 38)
m.addConstr(15*x0 + 16*x2 >= 43)
m.addConstr(12*x1 + x3 >= 91)
m.addConstr(15*x0 + 12*x1 >= 67)
m.addConstr(15*x0 + x3 >= 94)
m.addConstr(12*x1 + 16*x2 + x3 >= 96)
m.addConstr(15*x0 + 12*x1 + 16*x2 >= 96)
m.addConstr(12*x1 + 16*x2 + x3 >= 76)
m.addConstr(15*x0 + 12*x1 + 16*x2 >= 76)
m.addConstr(15*x0 + 12*x1 + 16*x2 + x3 >= 76)
m.addConstr(8*x1 + 11*x2 >= 146)
m.addConstr(11*x2 + 13*x3 >= 114)
m.addConstr(7*x0 + 8*x1 >= 140)
m.addConstr(7*x0 + 13*x3 >= 89)
m.addConstr(7*x0 + 8*x1 + 11*x2 >= 97)
m.addConstr(8*x1 + 11*x2 + 13*x3 >= 97)
m.addConstr(7*x0 + 8*x1 + 13*x3 >= 97)
m.addConstr(7*x0 + 8*x1 + 11*x2 >= 89)
m.addConstr(8*x1 + 11*x2 + 13*x3 >= 89)
m.addConstr(7*x0 + 8*x1 + 13*x3 >= 89)
m.addConstr(7*x0 + 8*x1 + 11*x2 >= 119)
m.addConstr(8*x1 + 11*x2 + 13*x3 >= 119)
m.addConstr(7*x0 + 8*x1 + 13*x3 >= 119)
m.addConstr(7*x0 + 8*x1 + 11*x2 + 13*x3 >= 119)
m.addConstr(13*x1 + 18*x3 <= 160)
m.addConstr(13*x1 + 4*x2 <= 251)
m.addConstr(x0 + 12*x3 <= 94)
m.addConstr(x0 + 24*x1 + 12*x3 <= 140)
m.addConstr(15*x0 + 16*x2 + x3 <= 349)
m.addConstr(7*x0 + 8*x1 + 11*x2 <= 359)
m.addConstr(8*x1 + 11*x2 + 13*x3 <= 536)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"x0: {x0.varValue}")
    print(f"x1: {x1.varValue}")
    print(f"x2: {x2.varValue}")
    print(f"x3: {x3.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```