Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

*  `x`: Number of small coffee pods
*  `y`: Number of large coffee pods

**Objective Function:**

Maximize profit: `3x + 5y`

**Constraints:**

* **Coffee Availability:** `15x + 20y <= 2000`
* **Small vs. Large Ratio:** `x >= 4y`
* **Minimum Large Pods:** `y >= 10`
* **Non-negativity:** `x >= 0`, `y >= 0`


```python
import gurobipy as gp
from gurobipy import GRB

# Create a new model
m = gp.Model("coffee_pods")

# Create variables
x = m.addVar(vtype=GRB.INTEGER, name="small_pods") # Number of small pods
y = m.addVar(vtype=GRB.INTEGER, name="large_pods") # Number of large pods

# Set objective function
m.setObjective(3*x + 5*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x + 20*y <= 2000, "coffee_availability")
m.addConstr(x >= 4*y, "small_large_ratio")
m.addConstr(y >= 10, "min_large_pods")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of small coffee pods (x): {x.x}")
    print(f"Number of large coffee pods (y): {y.x}")
    print(f"Maximum Profit: {m.objVal}")
elif m.status == GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization terminated with status: {m.status}")

```
