To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for the quantities of interest (acres of beans and peas), formulating the objective function based on the profit per acre for each crop, and establishing constraints related to the total available land and the bug repellant requirement.

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

The objective is to maximize profit. Given that the profit per acre of beans is $200 and the profit per acre of peas is $250, the objective function can be written as:
\[ \text{Maximize: } 200x_1 + 250x_2 \]

Constraints are based on two main factors: the total land available (100 acres) and the bug repellant limitation. The constraints can be formulated as follows:

1. **Total Land Constraint**: The sum of acres used for beans and peas cannot exceed 100 acres.
\[ x_1 + x_2 \leq 100 \]

2. **Bug Repellant Constraint**: Given that per acre of beans requires 12 liters of bug repellant and per acre of peas requires 15 liters, with a total of 1350 liters available, we have:
\[ 12x_1 + 15x_2 \leq 1350 \]

3. **Non-Negativity Constraints**: Since the number of acres cannot be negative, we also include:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Thus, the symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'acres of beans'), ('x2', 'acres of peas')],
  'objective_function': '200*x1 + 250*x2',
  'constraints': ['x1 + x2 <= 100', '12*x1 + 15*x2 <= 1350', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this linear programming problem, we will use Gurobi in Python. Here is the code to find the optimal solution:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="acres_of_beans")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="acres_of_peas")

# Set the objective function
m.setObjective(200*x1 + 250*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 100, "total_land_constraint")
m.addConstr(12*x1 + 15*x2 <= 1350, "bug_repellant_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Acres of beans: {x1.x}")
    print(f"Acres of peas: {x2.x}")
    print(f"Maximum profit: ${200*x1.x + 250*x2.x:.2f}")
else:
    print("No optimal solution found.")
```