To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints in algebraic terms.

Let's define:
- $x_1$ as the number of small coffee pods,
- $x_2$ as the number of large coffee pods.

The objective function, which aims to maximize profit, can be represented as:
\[ 3x_1 + 5x_2 \]

Given the constraints:
1. Total coffee available: $15x_1 + 20x_2 \leq 2000$,
2. At least 4 times as many small pods as large pods: $x_1 \geq 4x_2$,
3. At least 10 large coffee pods: $x_2 \geq 10$.

All variables are non-negative since they represent quantities of coffee pods.

In symbolic representation, the problem can be summarized as:
```json
{
    'sym_variables': [('x1', 'number of small coffee pods'), ('x2', 'number of large coffee pods')],
    'objective_function': '3*x1 + 5*x2',
    'constraints': ['15*x1 + 20*x2 <= 2000', 'x1 >= 4*x2', 'x2 >= 10', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we'll write the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="small_coffee_pods")
x2 = m.addVar(vtype=GRB.INTEGER, name="large_coffee_pods")

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

# Add constraints
m.addConstr(15*x1 + 20*x2 <= 2000, "coffee_availability")
m.addConstr(x1 >= 4*x2, "small_vs_large_ratio")
m.addConstr(x2 >= 10, "minimum_large_pods")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Small coffee pods: {x1.x}")
    print(f"Large coffee pods: {x2.x}")
    print(f"Maximum profit: ${3*x1.x + 5*x2.x:.2f}")
else:
    print("No optimal solution found")
```