## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'grams of protein' and 'milligrams of vitamin D'. Let's denote 'grams of protein' as $x_1$ and 'milligrams of vitamin D' as $x_2$. The objective function to minimize is $7x_1 + 3x_2$.

## Step 2: Translate the constraints into symbolic notation
The constraints given are:
1. $15x_1 + 14x_2 \geq 33$
2. $5x_1 + 25x_2 \geq 78$
3. $9x_1 - 6x_2 \geq 0$
4. $15x_1 + 14x_2 \leq 75$
5. $5x_1 + 25x_2 \leq 189$
6. $x_1$ is an integer.

## 3: Define the bounds for the variables
From the problem description, we have:
- $x_1 \geq 0$ (implicitly, as it's grams of protein)
- $x_2 \geq 0$ (implicitly, as it's milligrams of vitamin D)
- No upper bound is explicitly given for $x_1$ or $x_2$, but they are implicitly bounded by the constraints.

## 4: Create the symbolic representation
The symbolic representation of the problem is:
- Variables: $x_1$ (grams of protein), $x_2$ (milligrams of vitamin D)
- Objective function: Minimize $7x_1 + 3x_2$
- Constraints:
  1. $15x_1 + 14x_2 \geq 33$
  2. $5x_1 + 25x_2 \geq 78$
  3. $9x_1 - 6x_2 \geq 0$
  4. $15x_1 + 14x_2 \leq 75$
  5. $5x_1 + 25x_2 \leq 189$
  6. $x_1$ is an integer.

## 5: Convert to Gurobi code
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="grams_of_protein", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="milligrams_of_vitamin_D")

# Set the objective function
model.setObjective(7 * x1 + 3 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(15 * x1 + 14 * x2 >= 33, name="kidney_support_index_min")
model.addConstr(5 * x1 + 25 * x2 >= 78, name="cardiovascular_support_index_min")
model.addConstr(9 * x1 - 6 * x2 >= 0, name="protein_vitamin_D_balance")
model.addConstr(15 * x1 + 14 * x2 <= 75, name="kidney_support_index_max")
model.addConstr(5 * x1 + 25 * x2 <= 189, name="cardiovascular_support_index_max")

# Optimize the model
model.optimize()

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

## 6: Symbolic Representation in JSON format
```json
{
    "sym_variables": [
        ["x1", "grams of protein"],
        ["x2", "milligrams of vitamin D"]
    ],
    "objective_function": "7*x1 + 3*x2",
    "constraints": [
        "15*x1 + 14*x2 >= 33",
        "5*x1 + 25*x2 >= 78",
        "9*x1 - 6*x2 >= 0",
        "15*x1 + 14*x2 <= 75",
        "5*x1 + 25*x2 <= 189",
        "x1 is an integer"
    ]
}
```