To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- $x_1$ as the number of acres for growing carrots,
- $x_2$ as the number of acres for growing green peas.

The objective is to maximize profit. The profit per acre from carrots is $250, and from green peas is $340. Thus, the total profit can be represented by the objective function:
\[ \text{Maximize} \quad 250x_1 + 340x_2 \]

The constraints are based on the available days for watering and spraying bug repellant, as well as the total available land:
1. Watering constraint: It takes 0.7 days to water an acre of carrots and 0.4 days to water an acre of green peas. With 135 days available for watering, we have:
\[ 0.7x_1 + 0.4x_2 \leq 135 \]
2. Spraying bug repellant constraint: It takes 1.2 days to spray an acre of carrots and 1.5 days to spray an acre of green peas. With 110 days available for spraying, we have:
\[ 1.2x_1 + 1.5x_2 \leq 110 \]
3. Land constraint: The total land available is 100 acres, so:
\[ x_1 + x_2 \leq 100 \]
Additionally, $x_1$ and $x_2$ must be non-negative since they represent areas.

Thus, the symbolic representation of the problem in JSON format is:
```json
{
  'sym_variables': [('x1', 'acres of carrots'), ('x2', 'acres of green peas')],
  'objective_function': '250*x1 + 340*x2',
  'constraints': ['0.7*x1 + 0.4*x2 <= 135', '1.2*x1 + 1.5*x2 <= 110', 'x1 + x2 <= 100', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem in Gurobi using Python:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name='acres_of_carrots', lb=0)
x2 = m.addVar(name='acres_of_green_peas', lb=0)

# Set the objective function
m.setObjective(250*x1 + 340*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(0.7*x1 + 0.4*x2 <= 135, name='watering_constraint')
m.addConstr(1.2*x1 + 1.5*x2 <= 110, name='spraying_constraint')
m.addConstr(x1 + x2 <= 100, name='land_constraint')

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```