To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's denote the number of pills of type A as $x_1$ and the number of pills of type B as $x_2$. The objective is to minimize the total cost, which can be represented as $3x_1 + 5x_2$. The constraints are:

- Muscle relaxant: $2x_1 + 5x_2 \geq 30$
- Anxiety medication: $3x_1 + x_2 \geq 15$
- Pain reliever: $4x_1 + 3x_2 \geq 20$
- Non-negativity constraints: $x_1, x_2 \geq 0$

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of pills of type A'), ('x2', 'number of pills of type 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']
}
```

Now, let's write the Gurobi code in Python to solve this optimization problem:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="number_of_pills_A")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="number_of_pills_B")

# Set the objective function
m.setObjective(3*x1 + 5*x2, GRB.MINIMIZE)

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

# Optimize the model
m.optimize()

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