## Step 1: Define the symbolic representation of the variables
The variables are 'zucchini vines' and 'cucumber vines', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $2.44x_1 + 6.82x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $8x_1 + 15x_2 \geq 66$ (total combined resilience index must be 66 or more)
2. $6x_1 + x_2 \geq 66$ (total planting space must be 66 sq. ft or more)
3. $8x_1 - 3x_2 \geq 0$ (specific linear combination of vines)
4. $8x_1 + 15x_2 \leq 159$ (total combined resilience index must be 159 or less)
5. $6x_1 + x_2 \leq 172$ (total planting space must be 172 sq. ft or less, corrected from 159 ft^2 as per problem statement)
6. $x_1, x_2 \geq 0$ and are integers (whole number of vines)

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'zucchini vines'), ('x2', 'cucumber vines')],
'objective_function': '2.44*x1 + 6.82*x2',
'constraints': [
    '8*x1 + 15*x2 >= 66',
    '6*x1 + x2 >= 66',
    '8*x1 - 3*x2 >= 0',
    '8*x1 + 15*x2 <= 159',
    '6*x1 + x2 <= 172',
    'x1 >= 0', 'x2 >= 0', 'x1 % 1 == 0', 'x2 % 1 == 0'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="zucchini_vines", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="cucumber_vines", vtype=gurobi.GRB.INTEGER)

    # Objective function: minimize 2.44*x1 + 6.82*x2
    model.setObjective(2.44*x1 + 6.82*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(8*x1 + 15*x2 >= 66, name="resilience_index_min")
    model.addConstr(6*x1 + x2 >= 66, name="planting_space_min")
    model.addConstr(8*x1 - 3*x2 >= 0, name="linear_combination")
    model.addConstr(8*x1 + 15*x2 <= 159, name="resilience_index_max")
    model.addConstr(6*x1 + x2 <= 172, name="planting_space_max")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Zucchini vines: {x1.varValue}")
        print(f"Cucumber vines: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```