## Step 1: Define the variables and the objective function
The variables are ['grams of fat', 'milligrams of vitamin E', 'milligrams of vitamin B1', 'milligrams of vitamin A', 'milligrams of vitamin C']. Let's denote them as $x_0, x_1, x_2, x_3, x_4$ respectively.

## Step 2: Formulate the objective function
The objective function to maximize is:
\[ 1.83x_0^2 + 8.56x_0x_1 + 7.73x_0x_2 + 3.94x_0x_3 + 7.98x_0x_4 + 4.15x_1^2 + 1.78x_1x_2 + 2.28x_1x_3 + 7.57x_1x_4 + 3.2x_2^2 + 4.42x_2x_3 + 7.06x_2x_4 + 4.1x_3^2 + 8.39x_3x_4 + 6.68x_4^2 + 6.82x_0 + 8.6x_1 + 3.58x_2 + 6.45x_3 + 2.31x_4 \]

## 3: Define the constraints
The constraints are given based on the cardiovascular support index ($r_0$) and energy stability index ($r_1$) for each variable and combinations thereof.

## 4: Implement the constraints
Given:
- $r_0 = 4x_0 + 20x_1 + 26x_2 + 25x_3 + 22x_4$ with an upper bound of 391,
- $r_1 = 11x_0 + 20x_1 + 7x_2 + 29x_3 + 11x_4$ with an upper bound of 483,
- $x_2^2 + x_4^2 \geq 29$,
- $x_0^2 + x_3^2 \geq 28$,
- $x_0 + x_1 \geq 51$,
- $x_0^2 + x_1^2 + x_3^2 \geq 39$,
- $x_1 + x_2 + x_3 \geq 39$,
- $x_0 + x_1 + x_2 \geq 39$,
- $x_1 + x_2 + x_4 \geq 39$,
- $x_0^2 + x_1^2 + x_3^2 \geq 76$,
- $x_1 + x_2 + x_3 \geq 76$,
- $x_0 + x_1 + x_2 \geq 76$,
- $x_1 + x_2 + x_4 \geq 76$,
- $x_0 + x_1 + x_3 \geq 53$,
- $x_1 + x_2 + x_3 \geq 53$,
- $x_0 + x_1 + x_2 \geq 53$,
- $x_1 + x_2 + x_4 \geq 53$,
- $x_0 + x_1 + x_3 \geq 47$,
- $x_1 + x_2 + x_3 \geq 47$,
- $x_0^2 + x_1^2 + x_2^2 \geq 47$,
- $x_1 + x_2 + x_4 \geq 47$,
- $x_2^2 + x_3^2 \leq 324$,
- $x_1 + x_4 \leq 162$,
- $x_0 + x_1 \leq 322$,
- $x_0^2 + x_2^2 \leq 244$,
- $x_0 + x_1 + x_2 + x_3 + x_4 \leq 244$,
- $x_3 + x_4 \leq 240$,
- $x_1 + x_3 \leq 122$,
- $11x_0 + 20x_1 + 7x_2 + 29x_3 + 11x_4 \leq 122$.

## 5: Gurobi Code Implementation
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="grams of fat", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="milligrams of vitamin E", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="milligrams of vitamin B1")
x3 = m.addVar(name="milligrams of vitamin A")
x4 = m.addVar(name="milligrams of vitamin C")

# Objective function
obj = 1.83*x0**2 + 8.56*x0*x1 + 7.73*x0*x2 + 3.94*x0*x3 + 7.98*x0*x4 + 4.15*x1**2 + 1.78*x1*x2 + 2.28*x1*x3 + 7.57*x1*x4 + 3.2*x2**2 + 4.42*x2*x3 + 7.06*x2*x4 + 4.1*x3**2 + 8.39*x3*x4 + 6.68*x4**2 + 6.82*x0 + 8.6*x1 + 3.58*x2 + 6.45*x3 + 2.31*x4

# Set the objective
m.setObjective(obj, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(4*x0 + 20*x1 + 26*x2 + 25*x3 + 22*x4 <= 391, name="cardiovascular_support_index")
m.addConstr(11*x0 + 20*x1 + 7*x2 + 29*x3 + 11*x4 <= 483, name="energy_stability_index")

m.addConstr(x2**2 + x4**2 >= 29, name="combined_cardiovascular_support_index_B1_C")
m.addConstr(x0**2 + x3**2 >= 28, name="combined_cardiovascular_support_index_fat_A")
m.addConstr(x0 + x1 >= 51, name="combined_cardiovascular_support_index_fat_E")
m.addConstr(x0**2 + x1**2 + x3**2 >= 39, name="combined_cardiovascular_support_index_fat_E_A")
m.addConstr(x1 + x2 + x3 >= 39, name="combined_cardiovascular_support_index_E_B1_A")
m.addConstr(x0 + x1 + x2 >= 39, name="combined_cardiovascular_support_index_fat_E_B1")
m.addConstr(x1 + x2 + x4 >= 39, name="combined_cardiovascular_support_index_E_B1_C")

m.addConstr(x0**2 + x1**2 + x3**2 >= 76, name="combined_cardiovascular_support_index_fat_E_A_76")
m.addConstr(x1 + x2 + x3 >= 76, name="combined_cardiovascular_support_index_E_B1_A_76")
m.addConstr(x0 + x1 + x2 >= 76, name="combined_cardiovascular_support_index_fat_E_B1_76")
m.addConstr(x1 + x2 + x4 >= 76, name="combined_cardiovascular_support_index_E_B1_C_76")

m.addConstr(x0 + x1 + x3 >= 53, name="combined_cardiovascular_support_index_fat_E_A_53")
m.addConstr(x1 + x2 + x3 >= 53, name="combined_cardiovascular_support_index_E_B1_A_53")
m.addConstr(x0 + x1 + x2 >= 53, name="combined_cardiovascular_support_index_fat_E_B1_53")
m.addConstr(x1 + x2 + x4 >= 53, name="combined_cardiovascular_support_index_E_B1_C_53")

m.addConstr(x0 + x1 + x3 >= 47, name="combined_cardiovascular_support_index_fat_E_A_47")
m.addConstr(x1 + x2 + x3 >= 47, name="combined_cardiovascular_support_index_E_B1_A_47")
m.addConstr(x0**2 + x1**2 + x2**2 >= 47, name="combined_cardiovascular_support_index_fat_E_B1_47")
m.addConstr(x1 + x2 + x4 >= 47, name="combined_cardiovascular_support_index_E_B1_C_47")

m.addConstr(x2**2 + x3**2 <= 324, name="combined_cardiovascular_support_index_B1_A")
m.addConstr(x1 + x4 <= 162, name="combined_cardiovascular_support_index_E_C")
m.addConstr(x0 + x1 <= 322, name="combined_cardiovascular_support_index_fat_E")
m.addConstr(x0**2 + x2**2 <= 244, name="combined_cardiovascular_support_index_fat_B1")
m.addConstr(x0 + x1 + x2 + x3 + x4 <= 244, name="combined_cardiovascular_support_index_all")
m.addConstr(x3 + x4 <= 240, name="combined_energy_stability_index_A_C")
m.addConstr(x1 + x3 <= 122, name="combined_energy_stability_index_E_A")
m.addConstr(11*x0 + 20*x1 + 7*x2 + 29*x3 + 11*x4 <= 122, name="combined_energy_stability_index_all")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Grams of fat: ", x0.varValue)
    print("Milligrams of vitamin E: ", x1.varValue)
    print("Milligrams of vitamin B1: ", x2.varValue)
    print("Milligrams of vitamin A: ", x3.varValue)
    print("Milligrams of vitamin C: ", x4.varValue)
else:
    print("The model is infeasible.")
```