## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the acres of peas
- $x_2$ represents the acres of beans

## Step 2: Formulate the objective function
The profit per acre of peas is $100, and the profit per acre of beans is $160. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 100x_1 + 160x_2 \]

## 3: Define the constraints
1. Total acres constraint: The gardener has 30 acres available.
\[ x_1 + x_2 \leq 30 \]
2. Bug-spray constraint: The gardener has at most $1300 available for bug-spray.
\[ 30x_1 + 50x_2 \leq 1300 \]
3. Care-taking constraint: The gardener has 50 hours available for care-taking.
\[ 2x_1 + 1.5x_2 \leq 50 \]
4. Non-negativity constraints: The acres of peas and beans cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## 4: Symbolic representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'acres of peas'), ('x2', 'acres of beans')],
    'objective_function': '100*x1 + 160*x2',
    'constraints': [
        'x1 + x2 <= 30',
        '30*x1 + 50*x2 <= 1300',
        '2*x1 + 1.5*x2 <= 50',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi code
Now, let's implement this problem using Gurobi in Python:
```python
import gurobi

def solve_gardener_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="peas", lb=0, ub=None)
    x2 = model.addVar(name="beans", lb=0, ub=None)

    # Objective function: Maximize 100*x1 + 160*x2
    model.setObjective(100*x1 + 160*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 30, name="total_acres")
    model.addConstr(30*x1 + 50*x2 <= 1300, name="bug_spray_budget")
    model.addConstr(2*x1 + 1.5*x2 <= 50, name="care_taking_hours")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal acres of peas: {x1.varValue}")
        print(f"Optimal acres of beans: {x2.varValue}")
        print(f"Maximal profit: {model.objVal}")
    else:
        print("The problem is infeasible")

solve_gardener_problem()
```