## Step 1: Define the symbolic representation of the variables
The variables are defined as follows:
- $x_1$ : milligrams of vitamin B1
- $x_2$ : milligrams of zinc
- $x_3$ : milligrams of vitamin B7
- $x_4$ : grams of carbohydrates
- $x_5$ : milligrams of potassium
- $x_6$ : milligrams of vitamin B4

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is:
\[ 1x_1^2 + 8x_1x_2 + 6x_1x_4 + 2x_2^2 + 4x_2x_3 + 3x_2x_4 + 3x_3^2 + 3x_3x_4 + 4x_4^2 + 7x_4x_5 + 9x_5^2 + 3x_6^2 + 4x_1 + 8x_3 + 2x_4 + 3x_5 \]

## 3: List the constraints in symbolic notation
Constraints:
1. $5x_1 \leq 62$
2. $1x_2 \leq 62$
3. $3x_3 \leq 62$
4. $5x_4 \leq 62$
5. $5x_5 \leq 62$
6. $8x_6 \leq 62$
7. $5x_1 + 3x_3 \geq 6$
8. $5x_1 + 8x_6 \geq 7$
9. $5x_5^2 + 8x_6^2 \geq 9$
10. $3x_3 + 5x_4 \geq 10$
11. $1x_2 + 5x_4 \geq 5$
12. $3x_3 + 5x_5 \geq 9$
13. $x_2^2 + x_3^2 + x_6^2 \geq 10$
14. $x_3x_5x_6 \geq 10$
15. $x_2x_3x_5 \geq 10$
16. $x_1 + x_2 + x_3 \geq 10$
17. $x_3 + x_4 + x_6 \geq 10$
18. $x_1 + x_2 + x_5 \geq 10$
19. $x_2 + x_4 + x_6 \geq 10$
20. $x_3^2 + x_4^2 + x_5^2 \geq 10$
21. $x_2^2 + x_3^2 + x_6^2 \geq 10$
22. $x_3 + x_5 + x_6 \geq 10$
23. $x_2^2 + x_3^2 + x_5^2 \geq 10$
24. $x_1^2 + x_2^2 + x_3^2 \geq 10$
25. $x_3^2 + x_4^2 + x_6^2 \geq 10$
26. $x_1 + x_2 + x_5 \geq 10$
27. $x_2 + x_4 + x_6 \geq 10$
28. $x_3 + x_4 + x_5 \geq 10$
29. $x_2x_3x_6 \geq 10$
30. $x_3 + x_5 + x_6 \geq 10$
31. $x_2^2 + x_3^2 + x_5^2 \geq 10$
32. $x_1^2 + x_2^2 + x_3^2 \geq 10$
33. $x_3 + x_4 + x_6 \geq 10$
34. $x_1 + x_2 + x_5 \geq 10$
35. $x_2^2 + x_4^2 + x_6^2 \geq 10$
36. $x_3^2 + x_4^2 + x_5^2 \geq 9$
37. $x_2 + x_3 + x_5 \geq 9$
38. $x_1 + x_2 + x_3 \geq 9$
39. $x_3 + x_4 + x_6 \geq 9$
40. $x_1 + x_2 + x_5 \geq 9$
41. $x_2 + x_4 + x_6 \geq 9$
42. $x_3 + x_4 + x_5 \geq 9$
43. $x_2x_3x_6 \geq 9$
44. $x_3 + x_5 + x_6 \geq 9$
45. $x_2^2 + x_3^2 + x_5^2 \geq 9$
46. $x_1^2 + x_2^2 + x_3^2 \geq 9$
47. $-3x_2^2 + 9x_5^2 \geq 0$
48. $-x_4^2 + 6x_5^2 \geq 0$
49. $8x_3 - 5x_4 \geq 0$
50. $x_3 + x_4 \leq 20$
51. $x_2 + x_3 \leq 17$
52. $x_4 + x_6 \leq 57$
53. $x_3^2 + x_5^2 \leq 52$
54. $x_3 + x_6 \leq 59$
55. $x_2 + x_6 \leq 13$
56. $x_1 + x_5 \leq 57$
57. $x_1^2 + x_2^2 + x_6^2 \leq 13$
58. $x_1 + x_2 + x_5 \leq 15$

## 4: Gurobi Code

```python
import gurobi

def optimize():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1") # milligrams of vitamin B1
    x2 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="x2", vtype='I') # milligrams of zinc
    x3 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="x3", vtype='I') # milligrams of vitamin B7
    x4 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="x4", vtype='I') # grams of carbohydrates
    x5 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="x5", vtype='I') # milligrams of potassium
    x6 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="x6", vtype='I') # milligrams of vitamin B4

    # Objective function
    model.setObjective(1*x1**2 + 8*x1*x2 + 6*x1*x4 + 2*x2**2 + 4*x2*x3 + 3*x2*x4 + 3*x3**2 + 3*x3*x4 + 4*x4**2 + 7*x4*x5 + 9*x5**2 + 3*x6**2 + 4*x1 + 8*x3 + 2*x4 + 3*x5)

    # Constraints
    model.addConstr(5*x1 <= 62)
    model.addConstr(x2 <= 62)
    model.addConstr(3*x3 <= 62)
    model.addConstr(5*x4 <= 62)
    model.addConstr(5*x5 <= 62)
    model.addConstr(8*x6 <= 62)
    model.addConstr(5*x1 + 3*x3 >= 6)
    model.addConstr(5*x1 + 8*x6 >= 7)
    model.addConstr(5*x5**2 + 8*x6**2 >= 9)
    model.addConstr(3*x3 + 5*x4 >= 10)
    model.addConstr(x2 + 5*x4 >= 5)
    model.addConstr(3*x3 + 5*x5 >= 9)
    model.addConstr(x2**2 + x3**2 + x6**2 >= 10)
    model.addConstr(x3*x5*x6 >= 10)
    model.addConstr(x2*x3*x5 >= 10)
    model.addConstr(x1 + x2 + x3 >= 10)
    model.addConstr(x3 + x4 + x6 >= 10)
    model.addConstr(x1 + x2 + x5 >= 10)
    model.addConstr(x2 + x4 + x6 >= 10)
    model.addConstr(x3**2 + x4**2 + x5**2 >= 10)
    model.addConstr(x2**2 + x3**2 + x6**2 >= 10)
    model.addConstr(x3 + x5 + x6 >= 10)
    model.addConstr(x2**2 + x3**2 + x5**2 >= 10)
    model.addConstr(x1**2 + x2**2 + x3**2 >= 10)
    model.addConstr(x3**2 + x4**2 + x6**2 >= 10)
    model.addConstr(x1 + x2 + x5 >= 10)
    model.addConstr(x2 + x4 + x6 >= 10)
    model.addConstr(x3 + x4 + x5 >= 10)
    model.addConstr(x2*x3*x6 >= 10)
    model.addConstr(x3 + x5 + x6 >= 9)
    model.addConstr(x2**2 + x3**2 + x5**2 >= 9)
    model.addConstr(x1**2 + x2**2 + x3**2 >= 9)
    model.addConstr(-3*x2**2 + 9*x5**2 >= 0)
    model.addConstr(-x4**2 + 6*x5**2 >= 0)
    model.addConstr(8*x3 - 5*x4 >= 0)
    model.addConstr(x3 + x4 <= 20)
    model.addConstr(x2 + x3 <= 17)
    model.addConstr(x4 + x6 <= 57)
    model.addConstr(x3**2 + x5**2 <= 52)
    model.addConstr(x3 + x6 <= 59)
    model.addConstr(x2 + x6 <= 13)
    model.addConstr(x1 + x5 <= 57)
    model.addConstr(x1**2 + x2**2 + x6**2 <= 13)
    model.addConstr(x1 + x2 + x5 <= 15)

    model.optimize()

    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print("Objective: ", model.objVal)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
        print("x4: ", x4.varValue)
        print("x5: ", x5.varValue)
        print("x6: ", x6.varValue)
    else:
        print("No optimal solution found.")

optimize()
```

```json
{
    "sym_variables": [
        ["x1", "milligrams of vitamin B1"],
        ["x2", "milligrams of zinc"],
        ["x3", "milligrams of vitamin B7"],
        ["x4", "grams of carbohydrates"],
        ["x5", "milligrams of potassium"],
        ["x6", "milligrams of vitamin B4"]
    ],
    "objective_function": "1*x1^2 + 8*x1*x2 + 6*x1*x4 + 2*x2^2 + 4*x2*x3 + 3*x2*x4 + 3*x3^2 + 3*x3*x4 + 4*x4^2 + 7*x4*x5 + 9*x5^2 + 3*x6^2 + 4*x1 + 8*x3 + 2*x4 + 3*x5",
    "constraints": [
        "5*x1 <= 62",
        "x2 <= 62",
        "3*x3 <= 62",
        "5*x4 <= 62",
        "5*x5 <= 62",
        "8*x6 <= 62",
        "5*x1 + 3*x3 >= 6",
        "5*x1 + 8*x6 >= 7",
        "5*x5^2 + 8*x6^2 >= 9",
        "3*x3 + 5*x4 >= 10",
        "x2 + 5*x4 >= 5",
        "3*x3 + 5*x5 >= 9",
        "x2^2 + x3^2 + x6^2 >= 10",
        "x3*x5*x6 >= 10",
        "x2*x3*x5 >= 10",
        "x1 + x2 + x3 >= 10",
        "x3 + x4 + x6 >= 10",
        "x1 + x2 + x5 >= 10",
        "x2 + x4 + x6 >= 10",
        "x3^2 + x4^2 + x5^2 >= 10",
        "x2^2 + x3^2 + x6^2 >= 10",
        "x3 + x5 + x6 >= 10",
        "x2^2 + x3^2 + x5^2 >= 10",
        "x1^2 + x2^2 + x3^2 >= 10",
        "x3^2 + x4^2 + x6^2 >= 10",
        "x1 + x2 + x5 >= 10",
        "x2 + x4 + x6 >= 10",
        "x3 + x4 + x5 >= 10",
        "x2*x3*x6 >= 10",
        "x3 + x5 + x6 >= 9",
        "x2^2 + x3^2 + x5^2 >= 9",
        "x1^2 + x2^2 + x3^2 >= 9",
        "-3*x2^2 + 9*x5^2 >= 0",
        "-x4^2 + 6*x5^2 >= 0",
        "8*x3 - 5*x4 >= 0",
        "x3 + x4 <= 20",
        "x2 + x3 <= 17",
        "x4 + x6 <= 57",
        "x3^2 + x5^2 <= 52",
        "x3 + x6 <= 59",
        "x2 + x6 <= 13",
        "x1 + x5 <= 57",
        "x1^2 + x2^2 + x6^2 <= 13",
        "x1 + x2 + x5 <= 15"
    ]
}
```