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

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $9.11x_1 + 2.55x_2 + 5.21x_3 + 9.45x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $8x_1 + 7x_2 + 2x_3 + 15x_4 \geq 31$
- $8x_1 + 7x_2 \leq 89$
- $7x_2 + 2x_3 \leq 111$
- $8x_1 + 15x_4 \leq 95$
- $7x_2 + 15x_4 \leq 94$
- $8x_1 + 7x_2 + 15x_4 \leq 142$
- $8x_1 + 7x_2 + 2x_3 + 15x_4 \leq 142$

## 4: Consider the variable bounds and types
- $x_1$ is a continuous variable.
- $x_2$ is an integer variable.
- $x_3$ is a continuous variable.
- $x_4$ is a continuous variable.

## 5: Create the Gurobi model and variables
We will use Gurobi to solve this optimization problem.

## 6: Implement the Gurobi code
```python
import gurobi as gp

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

# Define the variables
x1 = m.addVar(lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, name="milligrams_of_vitamin_A")  # Continuous
x2 = m.addVar(lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, vtype=gp.GRB.INTEGER, name="milligrams_of_vitamin_B5")  # Integer
x3 = m.addVar(lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, name="grams_of_protein")  # Continuous
x4 = m.addVar(lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, name="grams_of_fat")  # Continuous

# Define the objective function
m.setObjective(9.11*x1 + 2.55*x2 + 5.21*x3 + 9.45*x4, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(8*x1 + 7*x2 + 2*x3 + 15*x4 >= 31, name="digestive_support_index_total")
m.addConstr(8*x1 + 7*x2 <= 89, name="vitamin_A_B5_digestive_support")
m.addConstr(7*x2 + 2*x3 <= 111, name="vitamin_B5_protein_digestive_support")
m.addConstr(8*x1 + 15*x4 <= 95, name="vitamin_A_fat_digestive_support")
m.addConstr(7*x2 + 15*x4 <= 94, name="vitamin_B5_fat_digestive_support")
m.addConstr(8*x1 + 7*x2 + 15*x4 <= 142, name="vitamin_A_B5_fat_digestive_support")
m.addConstr(8*x1 + 7*x2 + 2*x3 + 15*x4 <= 142, name="total_digestive_support")

# Solve the model
m.optimize()

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

## 7: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin A'), 
        ('x2', 'milligrams of vitamin B5'), 
        ('x3', 'grams of protein'), 
        ('x4', 'grams of fat')
    ], 
    'objective_function': '9.11*x1 + 2.55*x2 + 5.21*x3 + 9.45*x4', 
    'constraints': [
        '8*x1 + 7*x2 + 2*x3 + 15*x4 >= 31', 
        '8*x1 + 7*x2 <= 89', 
        '7*x2 + 2*x3 <= 111', 
        '8*x1 + 15*x4 <= 95', 
        '7*x2 + 15*x4 <= 94', 
        '8*x1 + 7*x2 + 15*x4 <= 142', 
        '8*x1 + 7*x2 + 2*x3 + 15*x4 <= 142'
    ]
}
```