## Step 1: Define the symbolic representation of the problem
The problem involves a patient who needs to consume milk and cheese to meet calcium and vitamin D requirements while minimizing cost. Let's define the symbolic variables:
- $x_1$ = servings of milk
- $x_2$ = servings of cheese

The objective is to minimize the cost, where a serving of milk costs $2 and a serving of cheese costs $4. Thus, the objective function is $2x_1 + 4x_2$.

## Step 2: Define the constraints based on the problem description
The patient must get at least 100 grams of calcium and 80 grams of Vitamin D per day. Given that:
- 1 serving of milk contains 10 grams of calcium and 5 grams of Vitamin D
- 1 serving of cheese contains 8 grams of calcium and 6 grams of Vitamin D

The constraints can be written as:
1. Calcium constraint: $10x_1 + 8x_2 \geq 100$
2. Vitamin D constraint: $5x_1 + 6x_2 \geq 80$
Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the patient cannot consume a negative number of servings.

## 3: Symbolic representation in JSON format
```json
{
'sym_variables': [('x1', 'servings of milk'), ('x2', 'servings of cheese')],
'objective_function': '2*x1 + 4*x2',
'constraints': [
    '10*x1 + 8*x2 >= 100',
    '5*x1 + 6*x2 >= 80',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 4: Convert the problem into Gurobi code in Python
```python
import gurobipy as gp

# Create a new model
model = gp.Model("Calcium_Vitamin_Optimization")

# Define the variables
x1 = model.addVar(name="milk", lb=0)  # servings of milk
x2 = model.addVar(name="cheese", lb=0)  # servings of cheese

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

# Define the constraints
model.addConstr(10*x1 + 8*x2 >= 100, name="calcium_constraint")
model.addConstr(5*x1 + 6*x2 >= 80, name="vitaminD_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Servings of milk: {x1.varValue}")
    print(f"Servings of cheese: {x2.varValue}")
    print(f"Total cost: ${2*x1.varValue + 4*x2.varValue:.2f}")
else:
    print("No optimal solution found.")
```