To solve the farmer's equipment allocation problem, we first need to define the decision variables and the constraints based on the given information. Let's denote:

- \(x_b\) as the number of acres allocated for beets.
- \(x_c\) as the number of acres allocated for carrots.

The objective is to maximize revenue, which can be calculated as \(200x_b + 340x_c\).

Now, let's consider the constraints based on the equipment availability and usage rates:

1. **Tractor Constraint**: The total time used by the tractor cannot exceed 10 hours. For beets, it requires 0.6 hours per acre, and for carrots, it requires 0.7 hours per acre.
   - \(0.6x_b + 0.7x_c \leq 10\)

2. **Plow Constraint**: The total time used by the plow cannot exceed 10 hours. For beets, it requires 0.3 hours per acre, and for carrots, it requires 0.25 hours per acre.
   - \(0.3x_b + 0.25x_c \leq 10\)

3. **Combine Constraint**: The total time used by the combine cannot exceed 10 hours. For beets, it requires 0.2 hours per acre, and for carrots, it requires 0.1 hours per acre.
   - \(0.2x_b + 0.1x_c \leq 10\)

4. **Non-Negativity Constraints**: The number of acres allocated to each farm cannot be negative.
   - \(x_b \geq 0\)
   - \(x_c \geq 0\)

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

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

# Define the decision variables
x_b = m.addVar(lb=0, name="acres_beets")
x_c = m.addVar(lb=0, name="acres_carrots")

# Define the objective function: Maximize revenue
m.setObjective(200*x_b + 340*x_c, GRB.MAXIMIZE)

# Add constraints
m.addConstr(0.6*x_b + 0.7*x_c <= 10, name="tractor_constraint")
m.addConstr(0.3*x_b + 0.25*x_c <= 10, name="plow_constraint")
m.addConstr(0.2*x_b + 0.1*x_c <= 10, name="combine_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Acreage of beets: {x_b.x}")
    print(f"Acreage of carrots: {x_c.x}")
    print(f"Maximum revenue: ${200*x_b.x + 340*x_c.x:.2f}")
else:
    print("No optimal solution found")

```