To solve this optimization problem, we need to define the decision variables, objective function, and constraints.

Let's denote:
- $I$ as the number of internet services installed,
- $T$ as the number of TV services installed.

The objective is to maximize profit. The profit per internet service installation is $100, and the profit per TV service installation is $120. Therefore, the total profit can be represented by the objective function:
\[ \text{Maximize:} \quad 100I + 120T \]

There are two types of constraints based on the available time for wiring and box installation:

1. **Wiring Time Constraint**: Each internet service takes 60 minutes of wiring time, and each TV service takes 50 minutes of wiring time. The company has 7000 minutes of wiring time available.
\[ 60I + 50T \leq 7000 \]

2. **Box Installation Time Constraint**: Each internet service takes 10 minutes of box installation time, and each TV service takes 20 minutes of box installation time. The company has 4000 minutes of box installation time available.
\[ 10I + 20T \leq 4000 \]

Additionally, the number of installations cannot be negative:
\[ I \geq 0 \]
\[ T \geq 0 \]

Now, let's translate this problem into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the decision variables
I = m.addVar(lb=0, vtype=GRB.INTEGER, name="Internet_Services")
T = m.addVar(lb=0, vtype=GRB.INTEGER, name="TV_Services")

# Set the objective function
m.setObjective(100*I + 120*T, GRB.MAXIMIZE)

# Add constraints
m.addConstr(60*I + 50*T <= 7000, "Wiring_Time_Constraint")
m.addConstr(10*I + 20*T <= 4000, "Box_Installation_Time_Constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Internet Services: {I.x}")
    print(f"TV Services: {T.x}")
    print(f"Maximum Profit: ${100*I.x + 120*T.x:.2f}")
else:
    print("No optimal solution found")
```