## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of calcium' and 'milligrams of vitamin B7'. Let's denote 'milligrams of calcium' as $x_1$ and 'milligrams of vitamin B7' as $x_2$. The objective function to minimize is $5.78x_1 + 5.62x_2$.

## 2: List the constraints in symbolic notation
The constraints given are:
- Kidney support index for $x_1$ is 13: $13x_1$
- Cognitive performance index for $x_1$ is 1: $1x_1$
- Muscle growth index for $x_1$ is 13: $13x_1$
- Kidney support index for $x_2$ is 11: $11x_2$
- Cognitive performance index for $x_2$ is 1: $1x_2$
- Muscle growth index for $x_2$ is 11: $11x_2$
- Total combined kidney support index $\geq 44$: $13x_1 + 11x_2 \geq 44$
- Total combined cognitive performance index $\geq 15$: $1x_1 + 1x_2 \geq 15$
- Total combined muscle growth index $\geq 13$: $13x_1 + 11x_2 \geq 13$
- $4x_1 - 9x_2 \geq 0$
- Total combined kidney support index $\leq 98$: $13x_1 + 11x_2 \leq 98$
- Total combined cognitive performance index $\leq 53$: $1x_1 + 1x_2 \leq 53$
- Total combined muscle growth index $\leq 34$: $13x_1 + 11x_2 \leq 34$
- $x_1$ is a whole number (integer)
- $x_2$ can be a non-integer

## 3: Convert the problem into a Gurobi-compatible format
We need to minimize $5.78x_1 + 5.62x_2$ subject to the constraints listed.

## 4: Write the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'milligrams of calcium'), ('x2', 'milligrams of vitamin B7')],
    'objective_function': '5.78*x1 + 5.62*x2',
    'constraints': [
        '13*x1 >= 13',
        '1*x1 >= 1',
        '13*x1 >= 13',
        '11*x2 >= 11',
        '1*x2 >= 1',
        '11*x2 >= 11',
        '13*x1 + 11*x2 >= 44',
        '1*x1 + 1*x2 >= 15',
        '13*x1 + 11*x2 >= 13',
        '4*x1 - 9*x2 >= 0',
        '13*x1 + 11*x2 <= 98',
        '1*x1 + 1*x2 <= 53',
        '13*x1 + 11*x2 <= 34'
    ]
}
```

## 5: Implement the problem in Gurobi
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="milligrams_of_calcium", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="milligrams_of_vitamin_B7")

    # Objective function
    model.setObjective(5.78 * x1 + 5.62 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(13 * x1 >= 13, name="kidney_support_calcium")
    model.addConstr(1 * x1 >= 1, name="cognitive_performance_calcium")
    model.addConstr(13 * x1 >= 13, name="muscle_growth_calcium")
    model.addConstr(11 * x2 >= 11, name="kidney_support_B7")
    model.addConstr(1 * x2 >= 1, name="cognitive_performance_B7")
    model.addConstr(11 * x2 >= 11, name="muscle_growth_B7")
    model.addConstr(13 * x1 + 11 * x2 >= 44, name="total_kidney_support_min")
    model.addConstr(1 * x1 + 1 * x2 >= 15, name="total_cognitive_performance_min")
    model.addConstr(13 * x1 + 11 * x2 >= 13, name="total_muscle_growth_min")
    model.addConstr(4 * x1 - 9 * x2 >= 0, name="calcium_B7_relation")
    model.addConstr(13 * x1 + 11 * x2 <= 98, name="total_kidney_support_max")
    model.addConstr(1 * x1 + 1 * x2 <= 53, name="total_cognitive_performance_max")
    model.addConstr(13 * x1 + 11 * x2 <= 34, name="total_muscle_growth_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 B7: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```