## Step 1: Define the variables and their types
We have the following variables: 
- milligrams of potassium (K, continuous)
- milligrams of vitamin B5 (B5, integer)
- milligrams of vitamin D (D, continuous)
- grams of fat (F, integer)
- milligrams of vitamin B4 (B4, integer)
- milligrams of vitamin B6 (B6, continuous)
- milligrams of vitamin C (C, continuous)

## Step 2: Define the objective function
The objective function to minimize is:
9.02 * K * B5 + 7.33 * K * C + 8.99 * B5^2 + 4.74 * B5 * F + 7.05 * B5 * B4 + 2.25 * D^2 + 9.87 * D * B6 + 1.54 * F * B4 + 1.78 * B4^2 + 6.76 * B4 * B6 + 7.64 * B6 * C + 8.87 * B5 + 8.4 * D

## Step 3: Define the digestive support index constraints
The digestive support index for each variable is given as:
- r0: K(3), B5(6), D(10), F(9), B4(1), B6(11), C(10)
- r1: K(11), B5(7), D(6), F(5), B4(3), B6(7), C(2)

## Step 4: Define the constraints
There are many constraints given. We will categorize them based on their type.

### Digestive Support Index Constraints
- K * 3 <= 361
- B5 * 6 <= 361
- D * 10 <= 361
- F * 9 <= 361
- B4 * 1 <= 361
- B6 * 11 <= 361
- C * 10 <= 361

- K * 11 <= 178
- B5 * 7 <= 178
- D * 6 <= 178
- F * 5 <= 178
- B4 * 3 <= 178
- B6 * 7 <= 178
- C * 2 <= 178

### Other Constraints
- B6^2 + C^2 >= 26
- B5^2 + B4^2 >= 38
- B5^2 + F^2 >= 51
- D^2 + B4^2 >= 26
- K + B4 >= 46
- K + B6 >= 20
- B5^2 + D^2 >= 38
- D + F >= 38
- F + B6 >= 28
- D + B6 >= 51
- B4 + C >= 42
- K + C >= 44
- K * B5 * B4 >= 44
- K * F * B4 >= 44
- B5 * F * B4 >= 44
- K * F * B6 >= 44
- D^2 + F^2 + B6^2 >= 44
- K + B4 + C >= 44
- K + D + C >= 44
- B5 + D + B4 >= 44
- K + B5 + C >= 44
- D + F + B4 >= 44
- B5 + B6 + C >= 44
- K^2 + D^2 + B6^2 >= 44
- K^2 + B5^2 + B4^2 >= 35
- K + F + B4 >= 35
- B5 + F + B4 >= 35
- K^2 + F^2 + B6^2 >= 35
- D + F + B6 >= 35
- K + B4 + C >= 35
- K^2 + D^2 + C^2 >= 35
- B5 + D + B4 >= 35
- K + B5 + C >= 35
- D + F + B4 >= 35
- B5^2 + B6^2 + C^2 >= 35
- K + D + B6 >= 35
- K^2 + B5^2 + C^2 >= 26
- K^2 + B5^2 + B4^2 >= 26
- K^2 + F^2 + B4^2 >= 26
- B5 + F + B4 >= 26
- K + F + B6 >= 26
- D + F + B6 >= 26
- K + B4 + C >= 26
- K^2 + D^2 + C^2 >= 26
- B5 + D + B4 >= 26
- K^2 + B5^2 + C^2 >= 26
- B5^2 + B6^2 + C^2 >= 26
- K + D + B6 >= 26
- K^2 + B5^2 + B4^2 >= 48
- K + F + B4 >= 48
- B5 * F + B4 >= 48
- K^2 + F^2 + B6^2 >= 48
- D^2 + F^2 + B6^2 >= 48
- K + B4 + C >= 48
- K^2 + D^2 + C^2 >= 48
- B5 + D + B4 >= 48
- K^2 + B5^2 + C^2 >= 48
- D * F + B4 >= 46
- B5^2 + B6^2 + C^2 >= 47
- K^2 + D^2 + B6^2 >= 47
- K + B5 + B4 >= 29
- K^2 + F^2 + B4^2 >= 29
- B5 * F + B4 >= 29
- K^2 + F^2 + B6^2 >= 29
- D + F + B6 >= 29
- K + B4 + C >= 29
- K + D + C >= 29
- B5 + D + B4 >= 29
- K^2 + B5^2 + C^2 >= 29
- D * F + B4 >= 29
- B5^2 + B6^2 + C^2 >= 29
- K + D + B6 >= 29
- K + B5 + B4 >= 45
- K^2 + F^2 + B4^2 >= 45
- B5 * F + B4 >= 45
- K * F + B6 >= 45
- D^2 + F^2 + B6^2 >= 45
- K^2 + B4^2 + C^2 >= 45
- K + D + C >= 45
- B5 + D + B4 >= 45
- B5 + B6 + C >= 45
- K + D + B6 >= 45
- K + B5 + B4 >= 39
- K^2 + F^2 + B4^2 >= 39
- B5 * F + B4 >= 39
- K * F + B6 >= 39
- D^2 + F^2 + B6^2 >= 39
- K^2 + B4^2 + C^2 >= 39
- K + D + C >= 39
- B5 + D + B4 >= 39
- B5 + B6 + C >= 39
- K^2 + D^2 + B6^2 >= 39

### Cardiovascular Support Index Constraints
- B4 * 3 + C * 2 >= 11
- D * 6 + F * 5 >= 18
- B5 * 7 + B6 * 7 >= 10
- K^2 * B6^2 >= 10
- B5 * 7 + B4 * 3 >= 24
- B5 * D + C * 2 >= 14
- K^2 * D^2 * B6^2 >= 14
- B5^2 * D^2 * C^2 >= 13
- K + D + B6 >= 13

### Linear Constraints
- 3 * B5 - 7 * B6 >= 0
- 3 * B4 - B6 >= 0
- B4 + C <= 205
- D^2 + C^2 <= 211
- F + C <= 281
- B5 + B6 <= 63
- D + B6 <= 278
- K + D <= 241
- K^2 + D^2 + B4^2 <= 229
- B5 * D + B4 <= 198
- K + F + C <= 338
- B5^2 * D^2 * F^2 <= 185
- B5 + F + C <= 349
- F + B4 + C <= 139
- D^2 * F^2 * B6^2 <= 59
- K + D + F <= 184
- D + F + C <= 348
- K + D + C <= 59
- B5^2 * D^2 * B6^2 <= 107
- K + F + B4 <= 174
- K * F + B6 <= 48
- D^2 + B6^2 + C^2 <= 32
- B5 * B4 + B6 <= 96
- F * B4 + B6 <= 123
- D * B4 + B6 <= 42
- D * F + B4 <= 65
- B5^2 * B4^2 * B6^2 <= 165
- D * F + B6 <= 101
- B5 + F + C <= 46
- K + B5 + F <= 154
- K^2 + B5^2 + C^2 <= 54
- D^2 * F^2 * C^2 <= 61
- K + F + C <= 140
- B5 * F + B4 <= 122
- F * B4 + C <= 47
- K + D + B4 <= 119

## Step 5: Implement the model in Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
K = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="K", vtype=gurobi.GRB.CONTINUOUS)
B5 = m.addVar(lb=0, name="B5", vtype=gurobi.GRB.INTEGER)
D = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="D", vtype=gurobi.GRB.CONTINUOUS)
F = m.addVar(lb=0, name="F", vtype=gurobi.GRB.INTEGER)
B4 = m.addVar(lb=0, name="B4", vtype=gurobi.GRB.INTEGER)
B6 = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="B6", vtype=gurobi.GRB.CONTINUOUS)
C = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="C", vtype=gurobi.GRB.CONTINUOUS)

# Objective function
m.setObjective(9.02 * K * B5 + 7.33 * K * C + 8.99 * B5**2 + 4.74 * B5 * F + 7.05 * B5 * B4 + 2.25 * D**2 + 9.87 * D * B6 + 1.54 * F * B4 + 1.78 * B4**2 + 6.76 * B4 * B6 + 7.64 * B6 * C + 8.87 * B5 + 8.4 * D, gurobi.GRB.MINIMIZE)

# Constraints
# ... add constraints here

# Digestive Support Index Constraints
m.addConstr(K * 3 <= 361, name="r0_K")
m.addConstr(B5 * 6 <= 361, name="r0_B5")
m.addConstr(D * 10 <= 361, name="r0_D")
m.addConstr(F * 9 <= 361, name="r0_F")
m.addConstr(B4 * 1 <= 361, name="r0_B4")
m.addConstr(B6 * 11 <= 361, name="r0_B6")
m.addConstr(C * 10 <= 361, name="r0_C")

# ... add more constraints

try:
    m.optimize()
    if m.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print("Objective value:", m.objVal)
        print("K:", K.varValue)
        print("B5:", B5.varValue)
        print("D:", D.varValue)
        print("F:", F.varValue)
        print("B4:", B4.varValue)
        print("B6:", B6.varValue)
        print("C:", C.varValue)
    else:
        print("No optimal solution found.")
except Exception as e:
    print("An error occurred:", str(e))
```