Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Number of boat trips
* `y`: Number of cargo plane trips

**Objective Function:**

Maximize the total number of boxes shipped: `500x + 200y`

**Constraints:**

* **Budget Constraint:** `5000x + 3000y <= 200000`
* **Boat Trip Limit:** `x <= y`
* **Non-negativity:** `x >= 0`, `y >= 0`

```python
import gurobipy as gp
from gurobipy import GRB

# Create a new model
m = gp.Model("LitchiShipping")

# Create variables
x = m.addVar(vtype=GRB.INTEGER, name="boat_trips")
y = m.addVar(vtype=GRB.INTEGER, name="plane_trips")

# Set objective function
m.setObjective(500 * x + 200 * y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5000 * x + 3000 * y <= 200000, "budget")
m.addConstr(x <= y, "trip_limit")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of boat trips: {x.x}")
    print(f"Number of plane trips: {y.x}")
    print(f"Total boxes shipped: {500 * x.x + 200 * y.x}")
elif m.status == GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
