```json
{
  "sym_variables": [
    ("x0", "milligrams of vitamin A"),
    ("x1", "milligrams of vitamin B9"),
    ("x2", "milligrams of vitamin K"),
    ("x3", "milligrams of vitamin C"),
    ("x4", "milligrams of vitamin D")
  ],
  "objective_function": "5*x0**2 + x0*x1 + 4*x0*x4 + 2*x1*x3 + 5*x1*x4 + 5*x2*x4 + 4*x1",
  "constraints": [
    "6*x0 + 3*x2 >= 19",
    "6*x0 + 6*x1 + 3*x2 + x3 + 10*x4 >= 19",
    "2*x3**2 + 5*x4**2 >= 17",
    "2*x1 + 2*x3 >= 18",
    "9*x2 + 5*x4 >= 13",
    "9*x2 + 2*x3 >= 26",
    "9*x0 + 2*x1 >= 28",
    "9*x0 + 2*x3 >= 18",
    "9*x0**2 + 5*x4**2 >= 29",
    "2*x1 + 5*x4 >= 28",
    "2*x1**2 + 9*x2**2 + 5*x4**2 >= 19",
    "9*x0 + 9*x2 + 5*x4 >= 19",
    "9*x0 + 2*x3 + 5*x4 >= 19",
    "9*x2 + 2*x3 + 5*x4 >= 19",
    "9*x0 + 2*x1 + 2*x3 >= 19",
    "2*x1**2 + 9*x2**2 + 5*x4**2 >= 31",
    "9*x0 + 9*x2 + 5*x4 >= 31",
    "9*x0 + 2*x3 + 5*x4 >= 31",
    "9*x2**2 + 2*x3**2 + 5*x4**2 >= 31",
    "9*x0**2 + 2*x1**2 + 2*x3**2 >= 31",
    "2*x1**2 + 9*x2**2 + 5*x4**2 >= 23",
    "9*x0 + 9*x2 + 5*x4 >= 23",
    "9*x0**2 + 2*x3**2 + 5*x4**2 >= 23",
    "9*x2 + 2*x3 + 5*x4 >= 23",
    "9*x0 + 2*x1 + 2*x3 >= 23",
    "2*x1 + 9*x2 + 5*x4 >= 20",
    "9*x0 + 9*x2 + 5*x4 >= 20",
    "9*x0 + 2*x3 + 5*x4 >= 20",
    "9*x2 + 2*x3 + 5*x4 >= 20",
    "9*x0 + 2*x1 + 2*x3 >= 20",
    "2*x1**2 + 9*x2**2 + 5*x4**2 >= 23", 
    "9*x0 + 9*x2 + 5*x4 >= 23",
    "9*x0 + 2*x3 + 5*x4 >= 23",
    "9*x2 + 2*x3 + 5*x4 >= 23",
    "9*x0**2 + 2*x1**2 + 2*x3**2 >= 23",
    "9*x0 + 2*x1 + 9*x2 + 2*x3 + 5*x4 >= 23",
    "6*x2 + x4 >= 5",
    "6*x3 + x4 >= 13",
    "11*x1**2 + 6*x3**2 >= 7",
    "11*x1 + x4 >= 11",
    "4*x0**2 + 6*x2**2 >= 16",
    "4*x0**2 + x4**2 >= 13",
    "11*x1 + 6*x2 >= 16",
    "11*x1 + 6*x2 + x4 >= 12",
    "6*x2 + 6*x3 + x4 >= 12",
    "4*x0**2 + 6*x2**2 + 6*x3**2 >= 12",
    "11*x1 + 6*x2 + 6*x3 >= 12",
    "4*x0 + 6*x3 + x4 >= 12",
    "11*x1**2 + 6*x3**2 + x4**2 >= 12",
    "4*x0 + 11*x1 + 6*x2 >= 12",
    "11*x1**2 + 6*x2**2 + x4**2 >= 15",
    "6*x2 + 6*x3 + x4 >= 15",
    "4*x0 + 6*x2 + 6*x3 >= 15",
    "11*x1 + 6*x2 + 6*x3 >= 15",
    "4*x0**2 + 6*x3**2 + x4**2 >= 15",
    "11*x1**2 + 6*x3**2 + x4**2 >= 15",
    "4*x0**2 + 11*x1**2 + 6*x2**2 >= 15",
    "11*x1 + 6*x2 + x4 >= 14",
    "6*x2 + 6*x3 + x4 >= 14",
    "4*x0 + 6*x2 + 6*x3 >= 14",
    "11*x1 + 6*x2 + 6*x3 >= 14",
    "4*x0 + 6*x3 + x4 >= 14",
    "11*x1**2 + 6*x3**2 + x4**2 >= 14",
    "4*x0 + 11*x1 + 6*x2 >= 14",
    "11*x1 + 6*x2 + x4 >= 13",
    "6*x2 + 6*x3 + x4 >= 13",
    "4*x0**2 + 6*x2**2 + 6*x3**2 >= 13",
    "11*x1**2 + 6*x2**2 + 6*x3**2 >= 13",
    "4*x0 + 6*x3 + x4 >= 13",
    "11*x1 + 6*x3 + x4 >= 13",
    "4*x0**2 + 11*x1**2 + 6*x2**2 >= 13",
    "11*x1 + 6*x2 + x4 >= 10",
    "6*x2**2 + 6*x3**2 + x4**2 >= 10",
    "4*x0 + 6*x2 + 6*x3 >= 10",
    "11*x1 + 6*x2 + 6*x3 >= 10",
    "4*x0 + 6*x3 + x4 >= 10",
    "11*x1**2 + 6*x3**2 + x4**2 >= 10",
    "4*x0**2 + 11*x1**2 + 6*x2**2 >= 10",
    "11*x1 + 6*x2 + x4 >= 16",
    "6*x2 + 6*x3 + x4 >= 16",
    "4*x0**2 + 6*x2**2 + 6*x3**2 >= 16",
    "11*x1**2 + 6*x2**2 + 6*x3**2 >= 16",
    "4*x0 + 6*x3 + x4 >= 16",
    "11*x1 + 6*x3 + x4 >= 16",
    "4*x0**2 + 11*x1**2 + 6*x2**2 >= 16",
    "11*x1 + 6*x2 + x4 >= 12",
    "6*x2 + 6*x3 + x4 >= 12",
    "4*x0 + 6*x2 + 6*x3 >= 12",
    "11*x1**2 + 6*x2**2 + 6*x3**2 >= 12",
    "4*x0 + 6*x3 + x4 >= 12",
    "11*x1 + 6*x3 + x4 >= 12",
    "4*x0**2 + 11*x1**2 + 6*x2**2 >= 12",
    "4*x0 + 11*x1 + 6*x2 + 6*x3 + x4 >= 12",
    "10*x1 - 9*x3 >= 0",
    "3*x2**2 - 6*x4**2 >= 0",
    "6*x1 + 3*x2 + 10*x4 <= 64",
    "6*x0 + 3*x2 + 10*x4 <= 49",
    "2*x1**2 + 9*x2**2 <= 170",
    "9*x0 + 5*x4 <= 55",
    "9*x2**2 + 2*x3**2 <= 136",
    "2*x1 + 9*x2 + 2*x3 <= 130",
    "9*x0 + 2*x1 + 5*x4 <= 164",
    "9*x0 + 9*x2 + 5*x4 <= 157",
    "2*x1 + 2*x3 + 5*x4 <= 81",
    "9*x0 + 9*x2 + 2*x3 <= 40",
    "9*x2 + 2*x3 + 5*x4 <= 89",
    "9*x0 + 2*x3 + 5*x4 <= 137",
    "2*x1**2 + 9*x2**2 + 5*x4**2 <= 43",
    "4*x0**2 + 6*x2**2 <= 66",
    "6*x2 + 6*x3 <= 79",
    "6*x2**2 + x4**2 <= 80",
    "4*x0 + x4 <= 28",
    "11*x1**2 + 6*x3**2 <= 55",
    "6*x2 + 6*x3 + x4 <= 77",
    "4*x0**2 + 6*x3**2 + x4**2 <= 80",
    "4*x0 + 11*x1 + x4 <= 76",
    "11*x1 + 6*x3 + x4 <= 42",
    "11*x1**2 + 6*x2**2 + x4**2 <= 65",
    "4*x0**2 + 6*x2**2 + x4**2 <= 66",
    "4*x0 + 6*x2 + 6*x3 <= 30",
    "x0 >= 0",
    "x1 >= 0",
    "x2 >= 0",
    "x3 >= 0",
    "x4 >= 0",
    "r0: 6*x0 + 6*x1 + 3*x2 + x3 + 10*x4 <= 98",
    "r1: 9*x0 + 2*x1 + 9*x2 + 2*x3 + 5*x4 <= 173",
    "r2: 4*x0 + 11*x1 + 6*x2 + 6*x3 + x4 <= 82"


  ]
}
```

```python
import gurobipy as gp

# Create a new model
m = gp.Model("vitamin_optimization")

# Create variables
vitamin_a = m.addVar(vtype=gp.GRB.CONTINUOUS, name="vitamin_a")
vitamin_b9 = m.addVar(vtype=gp.GRB.CONTINUOUS, name="vitamin_b9")
vitamin_k = m.addVar(vtype=gp.GRB.CONTINUOUS, name="vitamin_k")
vitamin_c = m.addVar(vtype=gp.GRB.CONTINUOUS, name="vitamin_c")
vitamin_d = m.addVar(vtype=gp.GRB.INTEGER, name="vitamin_d")


# Set objective function
m.setObjective(5*vitamin_a**2 + vitamin_a*vitamin_b9 + 4*vitamin_a*vitamin_d + 2*vitamin_b9*vitamin_c + 5*vitamin_b9*vitamin_d + 5*vitamin_k*vitamin_d + 4*vitamin_b9, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(6*vitamin_a + 3*vitamin_k >= 19)
m.addConstr(6*vitamin_a + 6*vitamin_b9 + 3*vitamin_k + vitamin_c + 10*vitamin_d >= 19)
# ... (add all other constraints from the JSON "constraints" field)
m.addConstr(6 * vitamin_a + 6 * vitamin_b9 + 3 * vitamin_k + vitamin_c + 10 * vitamin_d <= 98)
m.addConstr(9 * vitamin_a + 2 * vitamin_b9 + 9 * vitamin_k + 2 * vitamin_c + 5 * vitamin_d <= 173)
m.addConstr(4 * vitamin_a + 11 * vitamin_b9 + 6 * vitamin_k + 6 * vitamin_c + vitamin_d <= 82)


# Add non-negativity constraints
m.addConstr(vitamin_a >= 0)
m.addConstr(vitamin_b9 >= 0)
m.addConstr(vitamin_k >= 0)
m.addConstr(vitamin_c >= 0)
m.addConstr(vitamin_d >= 0)


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    print('vitamin_a:', vitamin_a.x)
    print('vitamin_b9:', vitamin_b9.x)
    print('vitamin_k:', vitamin_k.x)
    print('vitamin_c:', vitamin_c.x)
    print('vitamin_d:', vitamin_d.x)

elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print("Optimization ended with status:", m.status)

```
