To solve John's supplementation problem, we first need to translate the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of SD pills John should buy.
- $x_2$ as the number of LD pills John should buy.

The objective function aims to minimize the total cost. Given that each SD pill costs $1 and each LD pill costs $1.50, the objective function can be represented algebraically as:

\[ \text{Minimize:} \quad 1x_1 + 1.5x_2 \]

John needs at least 15 units of calcium and 20 units of iron every day. Since each SD pill contains 1 unit of calcium and 4 units of iron, and each LD pill contains 2 units of calcium and 1 unit of iron, we can represent these requirements as constraints:

- For calcium: $x_1 + 2x_2 \geq 15$
- For iron: $4x_1 + x_2 \geq 20$

Additionally, John cannot buy a negative number of pills, so we also have non-negativity constraints:

- $x_1 \geq 0$
- $x_2 \geq 0$

Symbolically representing the problem in the requested format gives us:
```json
{
    'sym_variables': [('x1', 'number of SD pills'), ('x2', 'number of LD pills')],
    'objective_function': 'Minimize: 1*x1 + 1.5*x2',
    'constraints': ['x1 + 2*x2 >= 15', '4*x1 + x2 >= 20', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we'll use the following code:
```python
from gurobipy import *

# Create a new model
m = Model("John_Supplementation")

# Add variables to the model
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="SD_pills", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="LD_pills", lb=0)

# Set the objective function
m.setObjective(1*x1 + 1.5*x2, GRB.MINIMIZE)

# Add constraints to the model
m.addConstr(x1 + 2*x2 >= 15, "Calcium_Constraint")
m.addConstr(4*x1 + x2 >= 20, "Iron_Constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of SD pills: {x1.x}")
    print(f"Number of LD pills: {x2.x}")
    print(f"Total cost: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```