To solve the optimization problem described, we will formulate a linear programming model. The goal is to maximize profit from growing corn and cabbage on 200 acres of land, given constraints on tractor time and hand-picking time.

Let's denote:
- \(x\) as the number of acres for corn.
- \(y\) as the number of acres for cabbage.

The objective function (to be maximized) represents the total profit from both crops. Given that corn yields $50 per acre and cabbage yields $70 per acre, we have:
\[ \text{Maximize:} \quad 50x + 70y \]

The constraints are as follows:

1. **Tractor Time Constraint**: It takes 1 day of tractor time for corn and 1.5 days for cabbage, with a total of 200 days available.
   \[ x + 1.5y \leq 200 \]

2. **Hand-picking Time Constraint**: It takes 2 days for corn and 3 days for cabbage, with a total of 275 days available.
   \[ 2x + 3y \leq 275 \]

3. **Land Availability Constraint**: The farmer has 200 acres in total.
   \[ x + y \leq 200 \]

4. **Non-Negativity Constraints**: Since the number of acres cannot be negative, we have:
   \[ x \geq 0, y \geq 0 \]

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

```python
from gurobipy import *

# Create a model
m = Model("Farm_Optimization")

# Define variables
x = m.addVar(name="corn_acres", vtype=GRB.CONTINUOUS, lb=0)
y = m.addVar(name="cabbage_acres", vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function (maximize profit)
m.setObjective(50*x + 70*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x + 1.5*y <= 200, name="tractor_time")
m.addConstr(2*x + 3*y <= 275, name="hand_picking_time")
m.addConstr(x + y <= 200, name="land_availability")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: x = {x.x}, y = {y.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```