## Step 1: Define the symbolic representation of the variables
The variables are defined as follows:
- $x_1$ represents milligrams of vitamin B5
- $x_2$ represents milligrams of vitamin B7
- $x_3$ represents grams of fiber
- $x_4$ represents milligrams of vitamin A

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is:
\[3x_1x_2 + 3x_1x_3 + 5x_1x_4 + 5x_2x_4 + 9x_3x_4 + 7x_2 + 2x_3\]

## 3: Define the constraints in symbolic notation
The constraints are:
1. $5x_1 \leq 71$
2. $5x_2 \leq 71$
3. $6x_3 \leq 71$
4. $4x_4 \leq 71$
5. $5x_1 + 6x_3 \geq 17$
6. $5x_1 + 5x_2 \geq 12$
7. $6x_3 + 4x_4 \geq 11$
8. $25x_2^2 + 16x_4^2 \geq 13$
9. $5x_1 + 5x_2 + 6x_3 \geq 12$
10. $5x_1 + 5x_2 + 4x_4 \geq 12$
11. $25x_1^2 + 25x_2^2 + 36x_3^2 \geq 17$
12. $25x_1^2 + 25x_2^2 + 16x_4^2 \geq 17$
13. $5x_1 + 6x_3 \leq 50$
14. $5x_1 + 5x_2 + 6x_3 + 4x_4 \leq 50$
15. $x_1$ is an integer
16. $x_2, x_3, x_4$ are continuous

## 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin B5'), 
        ('x2', 'milligrams of vitamin B7'), 
        ('x3', 'grams of fiber'), 
        ('x4', 'milligrams of vitamin A')
    ], 
    'objective_function': '3*x1*x2 + 3*x1*x3 + 5*x1*x4 + 5*x2*x4 + 9*x3*x4 + 7*x2 + 2*x3', 
    'constraints': [
        '5*x1 <= 71', 
        '5*x2 <= 71', 
        '6*x3 <= 71', 
        '4*x4 <= 71', 
        '5*x1 + 6*x3 >= 17', 
        '5*x1 + 5*x2 >= 12', 
        '6*x3 + 4*x4 >= 11', 
        '25*x2^2 + 16*x4^2 >= 13', 
        '5*x1 + 5*x2 + 6*x3 >= 12', 
        '5*x1 + 5*x2 + 4*x4 >= 12', 
        '25*x1^2 + 25*x2^2 + 36*x3^2 >= 17', 
        '25*x1^2 + 25*x2^2 + 16*x4^2 >= 17', 
        '5*x1 + 6*x3 <= 50', 
        '5*x1 + 5*x2 + 6*x3 + 4*x4 <= 50'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi as gp
from gurobi import GRB

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

# Define the variables
x1 = m.addVar(name="x1", vtype=GRB.INTEGER)  # milligrams of vitamin B5
x2 = m.addVar(name="x2")  # milligrams of vitamin B7
x3 = m.addVar(name="x3")  # grams of fiber
x4 = m.addVar(name="x4")  # milligrams of vitamin A

# Objective function
m.setObjective(3*x1*x2 + 3*x1*x3 + 5*x1*x4 + 5*x2*x4 + 9*x3*x4 + 7*x2 + 2*x3, GRB.MAXIMIZE)

# Constraints
m.addConstr(5*x1 <= 71)
m.addConstr(5*x2 <= 71)
m.addConstr(6*x3 <= 71)
m.addConstr(4*x4 <= 71)
m.addConstr(5*x1 + 6*x3 >= 17)
m.addConstr(5*x1 + 5*x2 >= 12)
m.addConstr(6*x3 + 4*x4 >= 11)
m.addConstr(25*x2**2 + 16*x4**2 >= 13)
m.addConstr(5*x1 + 5*x2 + 6*x3 >= 12)
m.addConstr(5*x1 + 5*x2 + 4*x4 >= 12)
m.addConstr(25*x1**2 + 25*x2**2 + 36*x3**2 >= 17)
m.addConstr(25*x1**2 + 25*x2**2 + 16*x4**2 >= 17)
m.addConstr(5*x1 + 6*x3 <= 50)
m.addConstr(5*x1 + 5*x2 + 6*x3 + 4*x4 <= 50)

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
    print("x4: ", x4.varValue)
else:
    print("The model is infeasible")
```