## Step 1: Define the variables and the objective function
The variables are ['milligrams of vitamin A', 'milligrams of vitamin B5', 'milligrams of iron', 'milligrams of vitamin B3', 'grams of carbohydrates']. Let's denote them as $x_0, x_1, x_2, x_3, x_4$ respectively.

The objective function to maximize is:
\[ 1.84x_0^2 + 7.25x_0x_1 + 2.77x_0x_3 + 8.72x_1^2 + 7.42x_1x_3 + 2.54x_1x_4 + 9.88x_2^2 + 5.3x_2x_4 + 3.67x_3^2 + 3.94x_3x_4 + 8.96x_4^2 + 7.01x_2 + 6.55x_4 \]

## Step 2: Define the constraints
The constraints are given as:
- $19x_0 \leq 237$
- $15x_1 \leq 237$
- $16x_2 \leq 237$
- $11x_3 \leq 237$
- $10x_4 \leq 237$
- $15x_1 + 10x_4 \geq 42$
- $15x_1 + 16x_2 \geq 32$
- $16x_2^2 + 11x_3^2 \geq 24$
- $16x_2 + 10x_4 \geq 47$
- $15x_1^2 + 11x_3^2 \geq 21$
- $19x_0 + 11x_3 \geq 23$
- $19x_0^2 + 15x_1^2 + 16x_2^2 \geq 30$
- $15x_1 + 16x_2 + 11x_3 \geq 30$
- $16x_2 + 11x_3 + 10x_4 \geq 30$
- $19x_0 + 15x_1 + 16x_2 \geq 23$
- $15x_1^2 + 16x_2^2 + 11x_3^2 \geq 23$
- $16x_2 + 11x_3 + 10x_4 \geq 23$
- $19x_0 + 15x_1 + 16x_2 \geq 42$
- $15x_1 + 16x_2 + 11x_3 \geq 42$
- $16x_2 + 11x_3 + 10x_4 \geq 42$
- $6x_0 - 10x_4 \geq 0$
- $11x_3 + 10x_4 \leq 218$
- $19x_0 + 15x_1 \leq 189$
- $15x_1^2 + 16x_2^2 + 10x_4^2 \leq 190$
- $16x_2^2 + 11x_3^2 + 10x_4^2 \leq 140$
- $15x_1 + 11x_3 + 10x_4 \leq 118$
- $19x_0^2 + 15x_1^2 + 16x_2^2 \leq 151$
- $15x_1 + 16x_2 + 11x_3 \leq 95$
- $19x_0 + 15x_1 + 16x_2 + 11x_3 + 10x_4 \leq 95$

## Step 3: Implement the problem in Gurobi
We will use Gurobi's Python interface to model and solve this problem.

```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(name="milligrams_of_vitamin_A", lb=-gp.GRB.INFINITY)
x1 = m.addVar(name="milligrams_of_vitamin_B5", lb=-gp.GRB.INFINITY)
x2 = m.addVar(name="milligrams_of_iron", lb=-gp.GRB.INFINITY)
x3 = m.addVar(name="milligrams_of_vitamin_B3", lb=-gp.GRB.INFINITY)
x4 = m.addVar(name="grams_of_carbohydrates", lb=-gp.GRB.INFINITY)

# Objective function
m.setObjective(1.84*x0**2 + 7.25*x0*x1 + 2.77*x0*x3 + 8.72*x1**2 + 7.42*x1*x3 + 2.54*x1*x4 + 
               9.88*x2**2 + 5.3*x2*x4 + 3.67*x3**2 + 3.94*x3*x4 + 8.96*x4**2 + 7.01*x2 + 6.55*x4, 
               sense=gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(19*x0 <= 237)
m.addConstr(15*x1 <= 237)
m.addConstr(16*x2 <= 237)
m.addConstr(11*x3 <= 237)
m.addConstr(10*x4 <= 237)

m.addConstr(15*x1 + 10*x4 >= 42)
m.addConstr(15*x1 + 16*x2 >= 32)
m.addConstr(16*x2**2 + 11*x3**2 >= 24)
m.addConstr(16*x2 + 10*x4 >= 47)
m.addConstr(15*x1**2 + 11*x3**2 >= 21)
m.addConstr(19*x0 + 11*x3 >= 23)
m.addConstr(19*x0**2 + 15*x1**2 + 16*x2**2 >= 30)
m.addConstr(15*x1 + 16*x2 + 11*x3 >= 30)
m.addConstr(16*x2 + 11*x3 + 10*x4 >= 30)
m.addConstr(19*x0 + 15*x1 + 16*x2 >= 23)
m.addConstr(15*x1**2 + 16*x2**2 + 11*x3**2 >= 23)
m.addConstr(16*x2 + 11*x3 + 10*x4 >= 23)
m.addConstr(19*x0 + 15*x1 + 16*x2 >= 42)
m.addConstr(15*x1 + 16*x2 + 11*x3 >= 42)
m.addConstr(16*x2 + 11*x3 + 10*x4 >= 42)
m.addConstr(6*x0 - 10*x4 >= 0)
m.addConstr(11*x3 + 10*x4 <= 218)
m.addConstr(19*x0 + 15*x1 <= 189)
m.addConstr(15*x1**2 + 16*x2**2 + 10*x4**2 <= 190)
m.addConstr(16*x2**2 + 11*x3**2 + 10*x4**2 <= 140)
m.addConstr(15*x1 + 11*x3 + 10*x4 <= 118)
m.addConstr(19*x0**2 + 15*x1**2 + 16*x2**2 <= 151)
m.addConstr(15*x1 + 16*x2 + 11*x3 <= 95)
m.addConstr(19*x0 + 15*x1 + 16*x2 + 11*x3 + 10*x4 <= 95)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Milligrams of vitamin A: {x0.varValue}")
    print(f"Milligrams of vitamin B5: {x1.varValue}")
    print(f"Milligrams of iron: {x2.varValue}")
    print(f"Milligrams of vitamin B3: {x3.varValue}")
    print(f"Grams of carbohydrates: {x4.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```