## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'hydrangeas', 'geraniums', 'bean stalks', and 'verbenas', which we can denote as $x_1, x_2, x_3,$ and $x_4$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $8x_1 + 7x_2 + 6x_3 + 6x_4$.

## 3: List the constraints in symbolic notation
The constraints given are:
- $11.64x_1 \geq 0$ (growth speed of hydrangeas, but this seems to be a characteristic rather than a constraint)
- $13.26x_1 \geq 0$ (resilience index of hydrangeas, similarly)
- $18.0x_2 \geq 0$ (growth speed of geraniums)
- $8.37x_2 \geq 0$ (resilience index of geraniums)
- $13.27x_3 \geq 0$ (growth speed of bean stalks)
- $2.51x_3 \geq 0$ (resilience index of bean stalks)
- $1.78x_4 \geq 0$ (growth speed of verbenas)
- $15.87x_4 \geq 0$ (resilience index of verbenas)
- $11.64x_1 + 18.0x_2 \geq 67$ (total growth speed of hydrangeas and geraniums)
- $13.26x_1 + 15.87x_4 \geq 38$ (total resilience index of hydrangeas and verbenas)
- $2.51x_3 + 15.87x_4 \geq 20$ (total resilience index of bean stalks and verbenas)
- $13.26x_1 + 2.51x_3 \geq 17$ (total resilience index of hydrangeas and bean stalks)
- $8.37x_2 + 2.51x_3 + 15.87x_4 \geq 29$ (total resilience index of geraniums, bean stalks, and verbenas)
- $13.26x_1 + 8.37x_2 + 2.51x_3 \geq 29$ (total resilience index of hydrangeas, geraniums, and bean stalks)
- $13.26x_1 + 2.51x_3 + 15.87x_4 \geq 29$ (total resilience index of hydrangeas, bean stalks, and verbenas)
- $8.37x_2 + 2.51x_3 + 15.87x_4 \geq 27$ (total resilience index of geraniums, bean stalks, and verbenas, alternative)
- $13.26x_1 + 8.37x_2 + 2.51x_3 \geq 27$ (total resilience index of hydrangeas, geraniums, and bean stalks, alternative)
- $13.26x_1 + 2.51x_3 + 15.87x_4 \geq 27$ (total resilience index of hydrangeas, bean stalks, and verbenas, alternative)
- $8.37x_2 + 2.51x_3 + 15.87x_4 \geq 25$ (total resilience index of geraniums, bean stalks, and verbenas, alternative)
- $13.26x_1 + 8.37x_2 + 2.51x_3 \geq 25$ (total resilience index of hydrangeas, geraniums, and bean stalks, alternative)
- $13.26x_1 + 2.51x_3 + 15.87x_4 \geq 25$ (total resilience index of hydrangeas, bean stalks, and verbenas, alternative)
- $13.27x_3 + 1.78x_4 \leq 241$ (total growth speed of bean stalks and verbenas)
- $11.64x_1 + 18.0x_2 \leq 175$ (total growth speed of hydrangeas and geraniums)
- $11.64x_1 + 13.27x_3 \leq 179$ (total growth speed of hydrangeas and bean stalks)
- $11.64x_1 + 1.78x_4 \leq 79$ (total growth speed of hydrangeas and verbenas)
- $11.64x_1 + 18.0x_2 + 13.27x_3 \leq 93$ (total growth speed of hydrangeas, geraniums, and bean stalks)
- $11.64x_1 + 13.27x_3 + 1.78x_4 \leq 154$ (total growth speed of hydrangeas, bean stalks, and verbenas)
- $11.64x_1 + 18.0x_2 + 13.27x_3 + 1.78x_4 \leq 154$ (total growth speed of all)
- $13.26x_1 + 15.87x_4 \leq 168$ (total resilience index of hydrangeas and verbenas)
- $8.37x_2 + 2.51x_3 \leq 52$ (total resilience index of geraniums and bean stalks)
- $2.51x_3 + 15.87x_4 \leq 129$ (total resilience index of bean stalks and verbenas)
- $13.26x_1 + 8.37x_2 + 2.51x_3 \leq 92$ (total resilience index of hydrangeas, geraniums, and bean stalks)
- $13.26x_1 + 2.51x_3 + 15.87x_4 \leq 110$ (total resilience index of hydrangeas, bean stalks, and verbenas)
- $13.26x_1 + 8.37x_2 + 2.51x_3 + 15.87x_4 \leq 110$ (total resilience index of all)

## 4: Define the symbolic variables and constraints for the Gurobi model
Given variables: 
- $x_1$ for hydrangeas
- $x_2$ for geraniums
- $x_3$ for bean stalks
- $x_4$ for verbenas

## 5: Formulate the Gurobi model
We will use Gurobi to solve this linear programming problem.

```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="hydrangeas", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="geraniums", vtype=gp.GRB.INTEGER)
x3 = m.addVar(name="bean_stalks", vtype=gp.GRB.INTEGER)
x4 = m.addVar(name="verbenas", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(8*x1 + 7*x2 + 6*x3 + 6*x4, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(11.64*x1 + 18.0*x2 >= 67)
m.addConstr(13.26*x1 + 15.87*x4 >= 38)
m.addConstr(2.51*x3 + 15.87*x4 >= 20)
m.addConstr(13.26*x1 + 2.51*x3 >= 17)
m.addConstr(8.37*x2 + 2.51*x3 + 15.87*x4 >= 29)
m.addConstr(13.26*x1 + 8.37*x2 + 2.51*x3 >= 29)
m.addConstr(13.26*x1 + 2.51*x3 + 15.87*x4 >= 29)
m.addConstr(8.37*x2 + 2.51*x3 + 15.87*x4 >= 27)
m.addConstr(13.26*x1 + 8.37*x2 + 2.51*x3 >= 27)
m.addConstr(13.26*x1 + 2.51*x3 + 15.87*x4 >= 27)
m.addConstr(8.37*x2 + 2.51*x3 + 15.87*x4 >= 25)
m.addConstr(13.26*x1 + 8.37*x2 + 2.51*x3 >= 25)
m.addConstr(13.26*x1 + 2.51*x3 + 15.87*x4 >= 25)
m.addConstr(13.27*x3 + 1.78*x4 <= 241)
m.addConstr(11.64*x1 + 18.0*x2 <= 175)
m.addConstr(11.64*x1 + 13.27*x3 <= 179)
m.addConstr(11.64*x1 + 1.78*x4 <= 79)
m.addConstr(11.64*x1 + 18.0*x2 + 13.27*x3 <= 93)
m.addConstr(11.64*x1 + 13.27*x3 + 1.78*x4 <= 154)
m.addConstr(11.64*x1 + 18.0*x2 + 13.27*x3 + 1.78*x4 <= 154)
m.addConstr(13.26*x1 + 15.87*x4 <= 168)
m.addConstr(8.37*x2 + 2.51*x3 <= 52)
m.addConstr(2.51*x3 + 15.87*x4 <= 129)
m.addConstr(13.26*x1 + 8.37*x2 + 2.51*x3 <= 92)
m.addConstr(13.26*x1 + 2.51*x3 + 15.87*x4 <= 110)
m.addConstr(13.26*x1 + 8.37*x2 + 2.51*x3 + 15.87*x4 <= 110)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hydrangeas: ", x1.varValue)
    print("Geraniums: ", x2.varValue)
    print("Bean Stalks: ", x3.varValue)
    print("Verbenas: ", x4.varValue)
else:
    print("The model is infeasible")
```

```json
{
    'sym_variables': [
        ('x1', 'hydrangeas'), 
        ('x2', 'geraniums'), 
        ('x3', 'bean stalks'), 
        ('x4', 'verbenas')
    ], 
    'objective_function': '8*x1 + 7*x2 + 6*x3 + 6*x4', 
    'constraints': [
        '11.64*x1 + 18.0*x2 >= 67', 
        '13.26*x1 + 15.87*x4 >= 38', 
        '2.51*x3 + 15.87*x4 >= 20', 
        '13.26*x1 + 2.51*x3 >= 17', 
        '8.37*x2 + 2.51*x3 + 15.87*x4 >= 29', 
        '13.26*x1 + 8.37*x2 + 2.51*x3 >= 29', 
        '13.26*x1 + 2.51*x3 + 15.87*x4 >= 29', 
        '8.37*x2 + 2.51*x3 + 15.87*x4 >= 27', 
        '13.26*x1 + 8.37*x2 + 2.51*x3 >= 27', 
        '13.26*x1 + 2.51*x3 + 15.87*x4 >= 27', 
        '8.37*x2 + 2.51*x3 + 15.87*x4 >= 25', 
        '13.26*x1 + 8.37*x2 + 2.51*x3 >= 25', 
        '13.26*x1 + 2.51*x3 + 15.87*x4 >= 25', 
        '13.27*x3 + 1.78*x4 <= 241', 
        '11.64*x1 + 18.0*x2 <= 175', 
        '11.64*x1 + 13.27*x3 <= 179', 
        '11.64*x1 + 1.78*x4 <= 79', 
        '11.64*x1 + 18.0*x2 + 13.27*x3 <= 93', 
        '11.64*x1 + 13.27*x3 + 1.78*x4 <= 154', 
        '11.64*x1 + 18.0*x2 + 13.27*x3 + 1.78*x4 <= 154', 
        '13.26*x1 + 15.87*x4 <= 168', 
        '8.37*x2 + 2.51*x3 <= 52', 
        '2.51*x3 + 15.87*x4 <= 129', 
        '13.26*x1 + 8.37*x2 + 2.51*x3 <= 92', 
        '13.26*x1 + 2.51*x3 + 15.87*x4 <= 110', 
        '13.26*x1 + 8.37*x2 + 2.51*x3 + 15.87*x4 <= 110'
    ]
}
```