To solve this optimization problem, we first need to define the decision variables, objective function, and constraints. The decision variables are \(x_1\) (the number of bottles of oolong tea made per day) and \(x_2\) (the number of bottles of green tea made per day). The objective is to maximize profit, given that the profit per bottle of oolong tea is $30 and per bottle of green tea is $20. Thus, the objective function can be written as:

\[ \text{Maximize} \quad 30x_1 + 20x_2 \]

The constraints are:
1. Demand for oolong tea: \(x_1 \leq 100\)
2. Demand for green tea: \(x_2 \leq 80\)
3. Supply constraint: \(x_1 + x_2 \leq 150\) (since the shop can make at most 150 bottles of either type each day)
4. Non-negativity constraints: \(x_1 \geq 0, x_2 \geq 0\) (since the number of bottles cannot be negative)

Given these definitions, we can now formulate the problem in Gurobi code to find the optimal values of \(x_1\) and \(x_2\).

```python
from gurobipy import *

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

# Define decision variables
x1 = m.addVar(lb=0, name="Oolong_Tea")
x2 = m.addVar(lb=0, name="Green_Tea")

# Define the objective function
m.setObjective(30*x1 + 20*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 100, "Demand_Oolong")
m.addConstr(x2 <= 80, "Demand_Green")
m.addConstr(x1 + x2 <= 150, "Supply_Constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Oolong Tea: {x1.x} bottles")
    print(f"Green Tea: {x2.x} bottles")
    print(f"Maximum Profit: ${30*x1.x + 20*x2.x}")
else:
    print("No optimal solution found.")
```