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

Let's denote:
- $C$ as the number of coffees sold,
- $H$ as the number of hot chocolates sold.

The objective is to maximize profit. Given that the profit on a coffee is $0.22 and on a hot chocolate is $0.14, the total profit can be represented by the equation: $0.22C + 0.14H$.

There are several constraints:
1. The vendor must sell at least 40 coffees: $C \geq 40$
2. The vendor must sell at least 20 hot chocolates: $H \geq 20$
3. The vendor cannot make more than 60 coffees: $C \leq 60$
4. The vendor cannot make more than 35 hot chocolates: $H \leq 35$
5. The total number of items sold cannot exceed 75: $C + H \leq 75$

This problem can be formulated as a linear programming problem, where we aim to maximize the profit under these constraints.

Here is how you can represent this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define the decision variables
C = m.addVar(lb=40, ub=60, vtype=GRB.INTEGER, name="coffees")
H = m.addVar(lb=20, ub=35, vtype=GRB.INTEGER, name="hot_chocolates")

# Define the objective function: maximize profit
m.setObjective(0.22*C + 0.14*H, GRB.MAXIMIZE)

# Add constraint for total items
m.addConstr(C + H <= 75, "total_items")

# Optimize model
m.optimize()

# Check if an optimal solution was found
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Coffees to sell: {C.x}")
    print(f"Hot chocolates to sell: {H.x}")
    print(f"Maximum profit: ${0.22*C.x + 0.14*H.x:.2f}")
else:
    print("No optimal solution found")
```