## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of calcium' and 'milligrams of vitamin E'. Let's denote 'milligrams of calcium' as $x_1$ and 'milligrams of vitamin E' as $x_2$. The objective function to minimize is $4x_1 + 5x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- $23x_1 + 1x_2 \geq 12$ (cardiovascular support index)
- $22x_1 + 7x_2 \geq 48$ (muscle growth index)
- $1x_1 + 21x_2 \geq 43$ (cognitive performance index)
- $26x_1 + 6x_2 \geq 7$ (immune support index)
- $6x_1 - 3x_2 \geq 0$
- $23x_1 + 1x_2 \leq 38$ (cardiovascular support index upper bound)
- $22x_1 + 7x_2 \leq 66$ (muscle growth index upper bound)
- $1x_1 + 21x_2 \leq 81$ (cognitive performance index upper bound)
- $26x_1 + 6x_2 \leq 31$ (immune support index upper bound)

## 3: Provide the symbolic representation of the problem
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'milligrams of calcium'), ('x2', 'milligrams of vitamin E')],
'objective_function': '4*x1 + 5*x2',
'constraints': [
    '23*x1 + 1*x2 >= 12',
    '22*x1 + 7*x2 >= 48',
    '1*x1 + 21*x2 >= 43',
    '26*x1 + 6*x2 >= 7',
    '6*x1 - 3*x2 >= 0',
    '23*x1 + 1*x2 <= 38',
    '22*x1 + 7*x2 <= 66',
    '1*x1 + 21*x2 <= 81',
    '26*x1 + 6*x2 <= 31'
]
}
```

## 4: Write the Gurobi code to solve the optimization problem
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="milligrams_of_calcium", lb=0)  # Assuming non-negative
    x2 = model.addVar(name="milligrams_of_vitamin_E", lb=0)  # Assuming non-negative

    # Define the objective function
    model.setObjective(4 * x1 + 5 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(23 * x1 + x2 >= 12, name="cardiovascular_support_index_min")
    model.addConstr(22 * x1 + 7 * x2 >= 48, name="muscle_growth_index_min")
    model.addConstr(x1 + 21 * x2 >= 43, name="cognitive_performance_index_min")
    model.addConstr(26 * x1 + 6 * x2 >= 7, name="immune_support_index_min")
    model.addConstr(6 * x1 - 3 * x2 >= 0, name="calcium_vitamin_E_balance")
    model.addConstr(23 * x1 + x2 <= 38, name="cardiovascular_support_index_max")
    model.addConstr(22 * x1 + 7 * x2 <= 66, name="muscle_growth_index_max")
    model.addConstr(x1 + 21 * x2 <= 81, name="cognitive_performance_index_max")
    model.addConstr(26 * x1 + 6 * x2 <= 31, name="immune_support_index_max")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of calcium: {x1.varValue}")
        print(f"Milligrams of vitamin E: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```