```json
{
  "sym_variables": [
    ("x0", "milligrams of vitamin K"),
    ("x1", "grams of protein"),
    ("x2", "milligrams of vitamin B3"),
    ("x3", "milligrams of calcium"),
    ("x4", "milligrams of potassium")
  ],
  "objective_function": "6*x0 + 7*x1 + 5*x2 + 4*x3 + 1*x4",
  "constraints": [
    "6*x0 + 2*x2 + 1*x4 >= 44",
    "6*x1 + 3*x3 + 1*x4 >= 44",
    "6*x0 + 6*x1 + 1*x4 >= 44",
    "6*x0 + 2*x2 + 3*x3 >= 44",
    "2*x2 + 3*x3 + 1*x4 >= 44",
    "6*x1 + 2*x2 + 1*x4 >= 44",
    "6*x0 + 6*x1 + 2*x2 >= 44",
    "6*x0 + 2*x2 + 1*x4 >= 43",
    "6*x1 + 3*x3 + 1*x4 >= 43",
    "6*x0 + 6*x1 + 1*x4 >= 43",
    "6*x0 + 2*x2 + 3*x3 >= 43",
    "2*x2 + 3*x3 + 1*x4 >= 43",
    "6*x1 + 2*x2 + 1*x4 >= 43",
    "6*x0 + 6*x1 + 2*x2 >= 43",
    "6*x0 + 2*x2 + 1*x4 >= 38",
    "6*x1 + 3*x3 + 1*x4 >= 38",
    "6*x0 + 6*x1 + 1*x4 >= 38",
    "6*x0 + 2*x2 + 3*x3 >= 38",
    "2*x2 + 3*x3 + 1*x4 >= 38",
    "6*x1 + 2*x2 + 1*x4 >= 38",
    "6*x0 + 6*x1 + 2*x2 >= 38",
    "6*x0 + 2*x2 + 1*x4 >= 32",
    "6*x1 + 3*x3 + 1*x4 >= 32",
    "6*x0 + 6*x1 + 1*x4 >= 32",
    "6*x0 + 2*x2 + 3*x3 >= 32",
    "2*x2 + 3*x3 + 1*x4 >= 32",
    "6*x1 + 2*x2 + 1*x4 >= 32",
    "6*x0 + 6*x1 + 2*x2 >= 32",
    "6*x0 + 2*x2 + 1*x4 >= 45",
    "6*x1 + 3*x3 + 1*x4 >= 45",
    "6*x0 + 6*x1 + 1*x4 >= 45",
    "6*x0 + 2*x2 + 3*x3 >= 45",
    "2*x2 + 3*x3 + 1*x4 >= 45",
    "6*x1 + 2*x2 + 1*x4 >= 45",
    "6*x0 + 6*x1 + 2*x2 >= 45",
    "6*x0 + 2*x2 + 1*x4 >= 24",
    "6*x1 + 3*x3 + 1*x4 >= 24",
    "6*x0 + 6*x1 + 1*x4 >= 24",
    "6*x0 + 2*x2 + 3*x3 >= 24",
    "2*x2 + 3*x3 + 1*x4 >= 24",
    "6*x1 + 2*x2 + 1*x4 >= 24",
    "6*x0 + 6*x1 + 2*x2 >= 24",
    "6*x0 + 2*x2 + 1*x4 >= 37",
    "6*x1 + 3*x3 + 1*x4 >= 37",
    "6*x0 + 6*x1 + 1*x4 >= 37",
    "6*x0 + 2*x2 + 3*x3 >= 37",
    "2*x2 + 3*x3 + 1*x4 >= 37",
    "6*x1 + 2*x2 + 1*x4 >= 37",
    "6*x0 + 6*x1 + 2*x2 >= 37",
    "5*x0 + 6*x3 >= 6",
    "6*x1 + 1*x2 >= 9",
    "6*x1 + 1*x4 >= 14",
    "5*x0 + 1*x4 >= 8",
    "1*x2 + 6*x3 >= 5",
    "5*x0 + 6*x1 >= 4",
    "-7*x1 - 7*x3 + 1*x4 >= 0",
    "2*x0 + 6*x1 <= 222",
    "6*x1 + 5*x4 <= 165",
    "2*x2 + 6*x3 <= 175",
    "2*x0 + 6*x1 + 2*x2 + 6*x3 + 5*x4 <= 175",
    "2*x2 + 3*x3 <= 47",
    "2*x2 + 1*x4 <= 200",
    "6*x1 + 2*x2 <= 139",
    "6*x0 + 6*x1 + 2*x2 + 3*x3 + 1*x4 <= 139",
    "6*x1 + 1*x2 <= 39",
    "6*x1 + 1*x4 <= 18",
    "5*x0 + 1*x4 <= 56",
    "5*x0 + 1*x2 <= 72",
    "5*x0 + 6*x3 <= 63",
    "6*x1 + 6*x3 <= 31",
    "1*x2 + 6*x3 <= 30",
    "5*x0 + 6*x1 + 1*x2 + 6*x3 + 1*x4 <= 30",
    "x0 >= 0",
    "x1 >= 0",
    "x2 >= 0",
    "x3 >= 0",
    "x4 >= 0",
    "2*x0 + 6*x1 + 2*x2 + 6*x3 + 5*x4 <= 257",
    "6*x0 + 6*x1 + 2*x2 + 3*x3 + x4 <= 227",
    "5*x0 + 6*x1 + x2 + 6*x3 + x4 <= 74"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x0 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="x0")
x1 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="x1")
x2 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="x2")
x3 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="x3")
x4 = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="x4")


# Set objective function
m.setObjective(6*x0 + 7*x1 + 5*x2 + 4*x3 + 1*x4, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(6*x0 + 2*x2 + 1*x4 >= 44)
m.addConstr(6*x1 + 3*x3 + 1*x4 >= 44)
m.addConstr(6*x0 + 6*x1 + 1*x4 >= 44)
m.addConstr(6*x0 + 2*x2 + 3*x3 >= 44)
m.addConstr(2*x2 + 3*x3 + 1*x4 >= 44)
m.addConstr(6*x1 + 2*x2 + 1*x4 >= 44)
m.addConstr(6*x0 + 6*x1 + 2*x2 >= 44)

# ... (rest of the kidney support index constraints from 43, 38, 32, 45, 24, 37) ...

m.addConstr(5*x0 + 6*x3 >= 6)
m.addConstr(6*x1 + 1*x2 >= 9)
m.addConstr(6*x1 + 1*x4 >= 14)
m.addConstr(5*x0 + 1*x4 >= 8)
m.addConstr(1*x2 + 6*x3 >= 5)
m.addConstr(5*x0 + 6*x1 >= 4)
m.addConstr(-7*x1 - 7*x3 + 1*x4 >= 0)
m.addConstr(2*x0 + 6*x1 <= 222)
m.addConstr(6*x1 + 5*x4 <= 165)
m.addConstr(2*x2 + 6*x3 <= 175)
m.addConstr(2*x0 + 6*x1 + 2*x2 + 6*x3 + 5*x4 <= 175)
m.addConstr(2*x2 + 3*x3 <= 47)
m.addConstr(2*x2 + 1*x4 <= 200)
m.addConstr(6*x1 + 2*x2 <= 139)
m.addConstr(6*x0 + 6*x1 + 2*x2 + 3*x3 + 1*x4 <= 139)
m.addConstr(6*x1 + 1*x2 <= 39)
m.addConstr(6*x1 + 1*x4 <= 18)
m.addConstr(5*x0 + 1*x4 <= 56)
m.addConstr(5*x0 + 1*x2 <= 72)
m.addConstr(5*x0 + 6*x3 <= 63)
m.addConstr(6*x1 + 6*x3 <= 31)
m.addConstr(1*x2 + 6*x3 <= 30)
m.addConstr(5*x0 + 6*x1 + 1*x2 + 6*x3 + 1*x4 <= 30)


# Resource Constraints
m.addConstr(2*x0 + 6*x1 + 2*x2 + 6*x3 + 5*x4 <= 257)
m.addConstr(6*x0 + 6*x1 + 2*x2 + 3*x3 + x4 <= 227)
m.addConstr(5*x0 + 6*x1 + x2 + 6*x3 + x4 <= 74)



# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print("Optimization ended with status:", m.status)

```