## Step 1: Define the symbolic representation of the variables
The variables are defined as follows:
- $x_1$ = milligrams of vitamin A
- $x_2$ = milligrams of vitamin B5
- $x_3$ = grams of carbohydrates
- $x_4$ = milligrams of vitamin E
- $x_5$ = milligrams of vitamin B4

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is: $5.59x_1 + 5.49x_2 + 3.39x_3 + 1.19x_4 + 8.96x_5$

## Step 3: List the constraints in symbolic notation
Constraints:
1. $8x_1 \leq 102$
2. $4x_1 \leq 112$
3. $1x_2 \leq 102$
4. $2x_2 \leq 112$
5. $4x_3 \leq 102$
6. $7x_3 \leq 112$
7. $5x_4 \leq 102$
8. $6x_4 \leq 112$
9. $5x_5 \leq 102$
10. $3x_5 \leq 112$
11. $8x_1 + 1x_2 \geq 18$
12. $8x_1 + 4x_3 \geq 11$
13. $4x_3 + 5x_4 \geq 19$
14. $1x_2 + 4x_3 + 5x_5 \geq 12$
15. $8x_1 + 1x_2 + 4x_3 + 5x_4 + 5x_5 \geq 12$
16. $2x_2 + 6x_4 \geq 15$
17. $2x_2 + 3x_5 \geq 11$
18. $7x_3 + 3x_5 \geq 22$
19. $4x_1 + 3x_5 \geq 22$
20. $4x_1 + 6x_4 \geq 19$
21. $4x_1 + 2x_2 \geq 21$
22. $2x_2 + 7x_3 + 6x_4 \geq 11$
23. $7x_3 + 6x_4 + 3x_5 \geq 11$
24. $4x_1 + 6x_4 + 3x_5 \geq 11$
25. $4x_1 + 2x_2 + 7x_3 \geq 11$
26. $2x_2 + 7x_3 + 6x_4 \geq 19$
27. $7x_3 + 6x_4 + 3x_5 \geq 19$
28. $4x_1 + 6x_4 + 3x_5 \geq 19$
29. $4x_1 + 2x_2 + 7x_3 \geq 19$
30. $2x_2 + 7x_3 + 6x_4 \geq 18$
31. $7x_3 + 6x_4 + 3x_5 \geq 18$
32. $4x_1 + 6x_4 + 3x_5 \geq 18$
33. $4x_1 + 2x_2 + 7x_3 \geq 18$
34. $4x_1 + 2x_2 + 7x_3 + 6x_4 + 3x_5 \geq 18$
35. $2x_3 - 4x_5 \geq 0$
36. $8x_1 + 4x_3 \leq 73$
37. $4x_3 + 5x_5 \leq 89$
38. $1x_2 + 4x_3 \leq 44$
39. $8x_1 + 1x_2 \leq 76$
40. $1x_2 + 5x_5 \leq 31$
41. $1x_2 + 4x_3 + 5x_4 \leq 52$
42. $2x_2 + 3x_5 \leq 65$
43. $4x_1 + 2x_2 \leq 28$
44. $7x_3 + 6x_4 \leq 95$
45. $2x_2 + 6x_4 \leq 92$
46. $2x_2 + 7x_3 \leq 36$
47. $4x_1 + 3x_5 \leq 39$
48. $4x_1 + 6x_4 \leq 94$

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin A'),
        ('x2', 'milligrams of vitamin B5'),
        ('x3', 'grams of carbohydrates'),
        ('x4', 'milligrams of vitamin E'),
        ('x5', 'milligrams of vitamin B4')
    ],
    'objective_function': '5.59*x1 + 5.49*x2 + 3.39*x3 + 1.19*x4 + 8.96*x5',
    'constraints': [
        '8*x1 <= 102',
        '4*x1 <= 112',
        '1*x2 <= 102',
        '2*x2 <= 112',
        '4*x3 <= 102',
        '7*x3 <= 112',
        '5*x4 <= 102',
        '6*x4 <= 112',
        '5*x5 <= 102',
        '3*x5 <= 112',
        '8*x1 + 1*x2 >= 18',
        '8*x1 + 4*x3 >= 11',
        '4*x3 + 5*x4 >= 19',
        '1*x2 + 4*x3 + 5*x5 >= 12',
        '8*x1 + 1*x2 + 4*x3 + 5*x4 + 5*x5 >= 12',
        '2*x2 + 6*x4 >= 15',
        '2*x2 + 3*x5 >= 11',
        '7*x3 + 3*x5 >= 22',
        '4*x1 + 3*x5 >= 22',
        '4*x1 + 6*x4 >= 19',
        '4*x1 + 2*x2 >= 21',
        '2*x2 + 7*x3 + 6*x4 >= 11',
        '7*x3 + 6*x4 + 3*x5 >= 11',
        '4*x1 + 6*x4 + 3*x5 >= 11',
        '4*x1 + 2*x2 + 7*x3 >= 11',
        '2*x2 + 7*x3 + 6*x4 >= 19',
        '7*x3 + 6*x4 + 3*x5 >= 19',
        '4*x1 + 6*x4 + 3*x5 >= 19',
        '4*x1 + 2*x2 + 7*x3 >= 19',
        '2*x2 + 7*x3 + 6*x4 >= 18',
        '7*x3 + 6*x4 + 3*x5 >= 18',
        '4*x1 + 6*x4 + 3*x5 >= 18',
        '4*x1 + 2*x2 + 7*x3 >= 18',
        '4*x1 + 2*x2 + 7*x3 + 6*x4 + 3*x5 >= 18',
        '2*x3 - 4*x5 >= 0',
        '8*x1 + 4*x3 <= 73',
        '4*x3 + 5*x5 <= 89',
        '1*x2 + 4*x3 <= 44',
        '8*x1 + 1*x2 <= 76',
        '1*x2 + 5*x5 <= 31',
        '1*x2 + 4*x3 + 5*x4 <= 52',
        '2*x2 + 3*x5 <= 65',
        '4*x1 + 2*x2 <= 28',
        '7*x3 + 6*x4 <= 95',
        '2*x2 + 6*x4 <= 92',
        '2*x2 + 7*x3 <= 36',
        '4*x1 + 3*x5 <= 39',
        '4*x1 + 6*x4 <= 94'
    ]
}
```

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

def optimize_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin A
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B5
    x3 = model.addVar(name="x3")  # grams of carbohydrates
    x4 = model.addVar(name="x4")  # milligrams of vitamin E
    x5 = model.addVar(name="x5")  # milligrams of vitamin B4

    # Define the objective function
    model.setObjective(5.59 * x1 + 5.49 * x2 + 3.39 * x3 + 1.19 * x4 + 8.96 * x5, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(8 * x1 <= 102)
    model.addConstr(4 * x1 <= 112)
    model.addConstr(1 * x2 <= 102)
    model.addConstr(2 * x2 <= 112)
    model.addConstr(4 * x3 <= 102)
    model.addConstr(7 * x3 <= 112)
    model.addConstr(5 * x4 <= 102)
    model.addConstr(6 * x4 <= 112)
    model.addConstr(5 * x5 <= 102)
    model.addConstr(3 * x5 <= 112)
    model.addConstr(8 * x1 + 1 * x2 >= 18)
    model.addConstr(8 * x1 + 4 * x3 >= 11)
    model.addConstr(4 * x3 + 5 * x4 >= 19)
    model.addConstr(1 * x2 + 4 * x3 + 5 * x5 >= 12)
    model.addConstr(8 * x1 + 1 * x2 + 4 * x3 + 5 * x4 + 5 * x5 >= 12)
    model.addConstr(2 * x2 + 6 * x4 >= 15)
    model.addConstr(2 * x2 + 3 * x5 >= 11)
    model.addConstr(7 * x3 + 3 * x5 >= 22)
    model.addConstr(4 * x1 + 3 * x5 >= 22)
    model.addConstr(4 * x1 + 6 * x4 >= 19)
    model.addConstr(4 * x1 + 2 * x2 >= 21)
    model.addConstr(2 * x2 + 7 * x3 + 6 * x4 >= 11)
    model.addConstr(7 * x3 + 6 * x4 + 3 * x5 >= 11)
    model.addConstr(4 * x1 + 6 * x4 + 3 * x5 >= 11)
    model.addConstr(4 * x1 + 2 * x2 + 7 * x3 >= 11)
    model.addConstr(2 * x2 + 7 * x3 + 6 * x4 >= 19)
    model.addConstr(7 * x3 + 6 * x4 + 3 * x5 >= 19)
    model.addConstr(4 * x1 + 6 * x4 + 3 * x5 >= 19)
    model.addConstr(4 * x1 + 2 * x2 + 7 * x3 >= 19)
    model.addConstr(2 * x2 + 7 * x3 + 6 * x4 >= 18)
    model.addConstr(7 * x3 + 6 * x4 + 3 * x5 >= 18)
    model.addConstr(4 * x1 + 6 * x4 + 3 * x5 >= 18)
    model.addConstr(4 * x1 + 2 * x2 + 7 * x3 >= 18)
    model.addConstr(4 * x1 + 2 * x2 + 7 * x3 + 6 * x4 + 3 * x5 >= 18)
    model.addConstr(2 * x3 - 4 * x5 >= 0)
    model.addConstr(8 * x1 + 4 * x3 <= 73)
    model.addConstr(4 * x3 + 5 * x5 <= 89)
    model.addConstr(1 * x2 + 4 * x3 <= 44)
    model.addConstr(8 * x1 + 1 * x2 <= 76)
    model.addConstr(1 * x2 + 5 * x5 <= 31)
    model.addConstr(1 * x2 + 4 * x3 + 5 * x4 <= 52)
    model.addConstr(2 * x2 + 3 * x5 <= 65)
    model.addConstr(4 * x1 + 2 * x2 <= 28)
    model.addConstr(7 * x3 + 6 * x4 <= 95)
    model.addConstr(2 * x2 + 6 * x4 <= 92)
    model.addConstr(2 * x2 + 7 * x3 <= 36)
    model.addConstr(4 * x1 + 3 * x5 <= 39)
    model.addConstr(4 * x1 + 6 * x4 <= 94)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"x1: {x1.varValue}")
        print(f"x2: {x2.varValue}")
        print(f"x3: {x3.varValue}")
        print(f"x4: {x4.varValue}")
        print(f"x5: {x5.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```