## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'milligrams of calcium', 'milligrams of vitamin E', and 'milligrams of vitamin D'. Let's denote these as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $4 \times \text{milligrams of calcium} + 3 \times \text{milligrams of vitamin E} + 2 \times \text{milligrams of vitamin D}$. In symbolic notation, this becomes $4x_1 + 3x_2 + 2x_3$.

## 3: Define the constraints in symbolic notation
The constraints given are:
1. $1x_1 \geq 0$ (muscle growth index for calcium, but it's given as 1 and no lower bound is specified, so we consider it as part of the attribute),
2. $2x_1$ (immune support index for calcium),
3. $10x_2$ (muscle growth index for vitamin E),
4. $10x_2$ (immune support index for vitamin E),
5. $10x_3$ (muscle growth index for vitamin D),
6. $2x_3$ (immune support index for vitamin D),
7. $10x_2 + 10x_3 \geq 44$,
8. $1x_1 + 10x_2 \geq 58$,
9. $1x_1 + 10x_3 \geq 54$,
10. $1x_1 + 10x_2 + 10x_3 \geq 39$,
11. $10x_2 + 2x_3 \geq 31$,
12. $2x_1 + 2x_3 \geq 74$,
13. $2x_1 + 10x_2 + 2x_3 \geq 74$,
14. $3x_1 - 9x_3 \geq 0$,
15. $-9x_1 + 5x_2 \geq 0$,
16. $2x_1 + 2x_3 \leq 189$,
17. $2x_1 + 10x_2 \leq 201$,
18. $10x_2 + 2x_3 \leq 117$,
19. $x_1$ is an integer (nonfractional),
20. $x_2$ is continuous (non-integer allowed),
21. $x_3$ is an integer.

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="milligrams_of_calcium", vtype=gurobi.GRB.INTEGER)  # integer
x2 = model.addVar(name="milligrams_of_vitamin_E", vtype=gurobi.GRB.CONTINUOUS)  # continuous
x3 = model.addVar(name="milligrams_of_vitamin_D", vtype=gurobi.GRB.INTEGER)  # integer

# Define the objective function
model.setObjective(4 * x1 + 3 * x2 + 2 * x3, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(10 * x2 + 10 * x3 >= 44)
model.addConstr(x1 + 10 * x2 >= 58)
model.addConstr(x1 + 10 * x3 >= 54)
model.addConstr(x1 + 10 * x2 + 10 * x3 >= 39)
model.addConstr(10 * x2 + 2 * x3 >= 31)
model.addConstr(2 * x1 + 2 * x3 >= 74)
model.addConstr(2 * x1 + 10 * x2 + 2 * x3 >= 74)
model.addConstr(3 * x1 - 9 * x3 >= 0)
model.addConstr(-9 * x1 + 5 * x2 >= 0)
model.addConstr(2 * x1 + 2 * x3 <= 189)
model.addConstr(2 * x1 + 10 * x2 <= 201)
model.addConstr(10 * x2 + 2 * x3 <= 117)

# 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"Milligrams of vitamin D: {x3.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 5: Symbolic representation in JSON format
```json
{
    "sym_variables": [
        ["x1", "milligrams of calcium"],
        ["x2", "milligrams of vitamin E"],
        ["x3", "milligrams of vitamin D"]
    ],
    "objective_function": "4*x1 + 3*x2 + 2*x3",
    "constraints": [
        "10*x2 + 10*x3 >= 44",
        "x1 + 10*x2 >= 58",
        "x1 + 10*x3 >= 54",
        "x1 + 10*x2 + 10*x3 >= 39",
        "10*x2 + 2*x3 >= 31",
        "2*x1 + 2*x3 >= 74",
        "2*x1 + 10*x2 + 2*x3 >= 74",
        "3*x1 - 9*x3 >= 0",
        "-9*x1 + 5*x2 >= 0",
        "2*x1 + 2*x3 <= 189",
        "2*x1 + 10*x2 <= 201",
        "10*x2 + 2*x3 <= 117"
    ]
}
```