To solve this optimization problem, we first need to define our decision variables, objective function, and constraints based on the given information.

Let's denote:
- $x$ as the number of Earl Grey teabags made,
- $y$ as the number of English Breakfast teabags made.

The objective is to maximize profit. Given that each Earl Grey teabag gives a profit of $0.30 and each English Breakfast teabag gives a profit of $0.25, our objective function can be written as:
\[ \text{Maximize:} \quad 0.30x + 0.25y \]

Now, let's define the constraints:

1. **Black Tea Availability Constraint**: Since there are only 3000 grams of black tea available, and each Earl Grey teabag requires 25 grams while each English Breakfast teabag requires 20 grams, we have:
\[ 25x + 20y \leq 3000 \]

2. **Demand Constraint**: At least 4 times the amount of Earl Grey teabags are needed than English Breakfast teabags:
\[ x \geq 4y \]

3. **Minimum English Breakfast Teabags Constraint**: At least 20 English Breakfast teabags need to be made:
\[ y \geq 20 \]

4. **Non-Negativity Constraints**: Since we cannot make a negative number of teabags, both $x$ and $y$ must be non-negative:
\[ x \geq 0, \quad y \geq 0 \]

Now, let's translate these constraints and the objective function into Gurobi code in Python:

```python
from gurobipy import *

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

# Define variables
x = m.addVar(name="Earl_Grey_Teabags", vtype=GRB.CONTINUOUS, lb=0)
y = m.addVar(name="English_Breakfast_Teabags", vtype=GRB.CONTINUOUS, lb=20)

# Set the objective function
m.setObjective(0.30*x + 0.25*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(25*x + 20*y <= 3000, name="Black_Tea_Availability")
m.addConstr(x >= 4*y, name="Demand_Constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal Solution Found:")
    print(f"Earl Grey Teabags: {x.x}")
    print(f"English Breakfast Teabags: {y.x}")
    print(f"Maximum Profit: ${0.30*x.x + 0.25*y.x:.2f}")
else:
    print("No optimal solution found")
```