## Problem Description and Formulation

The problem is a linear programming optimization problem. We need to maximize the profit from producing small and large coffee pods given certain constraints.

### Variables
- \(S\): Number of small coffee pods to be made.
- \(L\): Number of large coffee pods to be made.

### Objective Function
The profit per small coffee pod is $3, and the profit per large coffee pod is $5. The objective is to maximize the total profit \(P = 3S + 5L\).

### Constraints
1. **Coffee Availability**: There are only 2000 grams of coffee available. Each small coffee pod requires 15 grams, and each large coffee pod requires 20 grams. So, \(15S + 20L \leq 2000\).
2. **Small to Large Coffee Pod Ratio**: At least 4 times the amount of small coffee pods are needed than large coffee pods. So, \(S \geq 4L\).
3. **Minimum Large Coffee Pods**: At least 10 large coffee pods need to be made. So, \(L \geq 10\).
4. **Non-Negativity**: The number of coffee pods cannot be negative. So, \(S \geq 0\) and \(L \geq 0\).

## Gurobi Code

```python
import gurobi

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

    # Define variables
    S = model.addVar(name="Small_Coffee_Pods", vtype=gurobi.GRB.INTEGER, lb=0)
    L = model.addVar(name="Large_Coffee_Pods", vtype=gurobi.GRB.INTEGER, lb=10)

    # Objective function: Maximize profit
    model.setObjective(3 * S + 5 * L, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(15 * S + 20 * L <= 2000, name="Coffee_Availability")
    model.addConstr(S >= 4 * L, name="Small_to_Large_Ratio")

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Solution: Small Coffee Pods = {S.varValue}, Large Coffee Pods = {L.varValue}")
        print(f"Maximum Profit: ${model.objVal:.2f}")
    else:
        print("The model is infeasible.")

solve_coffee_pod_problem()
```