## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of vitamin D' and 'milligrams of zinc'. Let's denote 'milligrams of vitamin D' as $x_1$ and 'milligrams of zinc' as $x_2$. The objective function to minimize is $1 \cdot x_1 + 7 \cdot x_2$. The constraints are:
- $7x_1 \geq 7$ (cardiovascular support index for $x_1$)
- $7x_1 \geq 7$ (immune support index for $x_1$)
- $1x_2 \geq 1$ (cardiovascular support index for $x_2$)
- $2x_2 \geq 2$ (immune support index for $x_2$)
- $7x_1 + 1x_2 \geq 14$ (total combined cardiovascular support index)
- $7x_1 + 2x_2 \geq 24$ (total combined immune support index)
- $-7x_1 + 9x_2 \geq 0$
- $7x_1 + 1x_2 \leq 26$ (total combined cardiovascular support index upper bound)
- $7x_1 + 2x_2 \leq 32$ (total combined immune support index upper bound)
- $x_1$ is an integer
- $x_2$ can be any real number

## Step 2: Convert the problem into a symbolic representation
The symbolic variables are:
- $x_1$ for 'milligrams of vitamin D'
- $x_2$ for 'milligrams of zinc'

The objective function is: $x_1 + 7x_2$

The constraints in symbolic form are:
1. $7x_1 \geq 7$
2. $7x_1 \geq 7$
3. $x_2 \geq 1$
4. $2x_2 \geq 2$
5. $7x_1 + x_2 \geq 14$
6. $7x_1 + 2x_2 \geq 24$
7. $-7x_1 + 9x_2 \geq 0$
8. $7x_1 + x_2 \leq 26$
9. $7x_1 + 2x_2 \leq 32$
10. $x_1 \in \mathbb{Z}$
11. $x_2 \in \mathbb{R}$

## 3: Simplify the constraints
Some constraints can be simplified:
- From constraint 3 and 4, we get $x_2 \geq 1$ and $x_2 \geq 1$, so $x_2 \geq 1$ is sufficient.
- Constraints 1 and 2 are the same: $7x_1 \geq 7$ or $x_1 \geq 1$.

## 4: Write down the problem in a standard optimization format
Minimize: $x_1 + 7x_2$

Subject to:
- $x_1 \geq 1$
- $x_2 \geq 1$
- $7x_1 + x_2 \geq 14$
- $7x_1 + 2x_2 \geq 24$
- $-7x_1 + 9x_2 \geq 0$
- $7x_1 + x_2 \leq 26$
- $7x_1 + 2x_2 \leq 32$
- $x_1 \in \mathbb{Z}$
- $x_2 \in \mathbb{R}$

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

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

# Define the variables
x1 = model.addVar(lb=1, vtype=gurobi.GRB.INTEGER, name="x1")  # milligrams of vitamin D
x2 = model.addVar(lb=1, name="x2")  # milligrams of zinc

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

# Add constraints
model.addConstr(7 * x1 + x2 >= 14, name="cardiovascular_support")
model.addConstr(7 * x1 + 2 * x2 >= 24, name="immune_support")
model.addConstr(-7 * x1 + 9 * x2 >= 0, name="zinc_vs_vitaminD")
model.addConstr(7 * x1 + x2 <= 26, name="cardiovascular_upper_bound")
model.addConstr(7 * x1 + 2 * x2 <= 32, name="immune_upper_bound")

# Optimize the model
model.optimize()

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

## 6: Provide the symbolic representation in JSON format
```json
{
    "sym_variables": [
        ["x1", "milligrams of vitamin D"],
        ["x2", "milligrams of zinc"]
    ],
    "objective_function": "x1 + 7*x2",
    "constraints": [
        "x1 >= 1",
        "x2 >= 1",
        "7*x1 + x2 >= 14",
        "7*x1 + 2*x2 >= 24",
        "-7*x1 + 9*x2 >= 0",
        "7*x1 + x2 <= 26",
        "7*x1 + 2*x2 <= 32"
    ]
}
```