To solve this optimization problem, we first need to define the decision variables and the objective function. Let's denote:

- \(x_s\) as the number of small coffee pods made,
- \(x_l\) as the number of large coffee pods made.

The objective is to maximize profit, given by \(3x_s + 5x_l\), since each small pod brings in $3 and each large pod brings in $5.

We have several constraints:

1. **Coffee Availability Constraint**: The total amount of coffee used cannot exceed 2000 grams. Given that each small coffee pod requires 15 grams and each large coffee pod requires 20 grams, we can express this as \(15x_s + 20x_l \leq 2000\).

2. **Small Pods to Large Pods Ratio Constraint**: At least 4 times the amount of small coffee pods are needed than large coffee pods, which can be expressed as \(x_s \geq 4x_l\).

3. **Minimum Large Coffee Pods Constraint**: At least 10 large coffee pods need to be made, so \(x_l \geq 10\).

All variables (\(x_s\) and \(x_l\)) must be non-negative since we cannot produce a negative number of pods.

Now, let's translate these conditions into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the decision variables
x_s = m.addVar(vtype=GRB.INTEGER, name="small_pods")
x_l = m.addVar(vtype=GRB.INTEGER, name="large_pods")

# Objective function: Maximize profit
m.setObjective(3*x_s + 5*x_l, GRB.MAXIMIZE)

# Constraints
m.addConstr(15*x_s + 20*x_l <= 2000, "coffee_availability")
m.addConstr(x_s >= 4*x_l, "small_to_large_ratio")
m.addConstr(x_l >= 10, "minimum_large_pods")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Small pods: {x_s.x}")
    print(f"Large pods: {x_l.x}")
    print(f"Max Profit: {m.objVal}")
else:
    print("No optimal solution found")
```