## Step 1: Define the symbolic representation of the problem
Let's denote the number of Pill A to be bought as $x_1$ and the number of Pill B to be bought as $x_2$. The objective is to minimize the total cost, which is $3x_1 + 5x_2$. The constraints based on the requirements are:
- Muscle relaxant: $2x_1 + 5x_2 \geq 30$
- Anxiety medication: $3x_1 + x_2 \geq 15$
- Pain reliever: $4x_1 + 3x_2 \geq 20$
Also, $x_1 \geq 0$ and $x_2 \geq 0$ since the number of pills cannot be negative.

## 2: Convert the problem into a symbolic representation
The symbolic variables are:
- $x_1$ for Pill A
- $x_2$ for Pill B

The objective function to minimize is: $3x_1 + 5x_2$

The constraints are:
- $2x_1 + 5x_2 \geq 30$
- $3x_1 + x_2 \geq 15$
- $4x_1 + 3x_2 \geq 20$
- $x_1 \geq 0$
- $x_2 \geq 0$

## 3: Represent the problem in the required JSON format
```json
{
'sym_variables': [('x1', 'Pill A'), ('x2', 'Pill B')],
'objective_function': '3*x1 + 5*x2',
'constraints': [
    '2*x1 + 5*x2 >= 30',
    '3*x1 + x2 >= 15',
    '4*x1 + 3*x2 >= 20',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 4: Implement the problem in Gurobi code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="x1", lb=0, vtype=gurobi.GRB.CONTINUOUS)  # Pill A
    x2 = model.addVar(name="x2", lb=0, vtype=gurobi.GRB.CONTINUOUS)  # Pill B

    # Define the objective function
    model.setObjective(3*x1 + 5*x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(2*x1 + 5*x2 >= 30, name="muscle_relaxant")
    model.addConstr(3*x1 + x2 >= 15, name="anxiety_medication")
    model.addConstr(4*x1 + 3*x2 >= 20, name="pain_reliever")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Pill A: {x1.varValue}")
        print(f"Pill B: {x2.varValue}")
        print(f"Total cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```