## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are 'roses', 'chili plants', 'chrysanthemums', 'pansies', and 'tomato vines', which we can denote as $x_1, x_2, x_3, x_4, x_5$ respectively.

## Step 2: Formulate the objective function
The objective function to minimize is $6.17x_1 + 2.7x_2 + 5.24x_3 + 9.67x_4 + 1.02x_5$.

## 3: Define the constraints
The constraints are:
- $14x_1 + 2x_4 \geq 22$
- $17x_2 + 2x_4 \geq 21$
- $14x_1 + 11x_5 \geq 26$
- $14x_1 + 17x_2 \geq 12$
- $14x_1 + 13x_3 \geq 13$
- $14x_1 + 17x_2 + 13x_3 + 2x_4 + 11x_5 \geq 13$
- $11x_2 + 4x_5 \geq 41$
- $2x_1 + 7x_4 \geq 39$
- $2x_1 + 11x_2 \geq 23$
- $11x_2 + 17x_3 \geq 39$
- $11x_2 + 7x_4 \geq 49$
- $2x_1 + 4x_5 \geq 33$
- $17x_3 + 7x_4 \geq 20$
- $7x_4 + 4x_5 \geq 38$
- $11x_2 + 17x_3 + 7x_4 \geq 38$
- $11x_2 + 17x_3 + 4x_5 \geq 38$
- $2x_1 + 11x_2 + 17x_3 \geq 38$
- $17x_3 + 7x_4 + 4x_5 \geq 38$
- $2x_1 + 17x_3 + 4x_5 \geq 38$
- $2x_1 + 17x_3 + 7x_4 \geq 38$
- $2x_1 + 11x_2 + 7x_4 \geq 38$
- $11x_2 + 17x_3 + 4x_5 \geq 45$
- $11x_2 + 17x_3 + 7x_4 \geq 45$
- $2x_1 + 11x_2 + 17x_3 \geq 45$
- $17x_3 + 7x_4 + 4x_5 \geq 45$
- $2x_1 + 17x_3 + 4x_5 \geq 45$
- $2x_1 + 17x_3 + 7x_4 \geq 45$
- $2x_1 + 11x_2 + 7x_4 \geq 45$
- $11x_2 + 17x_3 + 7x_4 \geq 41$
- $11x_2 + 17x_3 + 4x_5 \geq 41$
- $2x_1 + 11x_2 + 17x_3 \geq 41$
- $17x_3 + 7x_4 + 4x_5 \geq 41$
- $2x_1 + 17x_3 + 4x_5 \geq 41$
- $2x_1 + 17x_3 + 7x_4 \geq 41$
- $2x_1 + 11x_2 + 7x_4 \geq 41$
- $2x_1 + 17x_3 + 7x_4 \geq 31$
- $2x_1 + 11x_2 + 17x_3 \geq 31$
- $17x_3 + 7x_4 + 4x_5 \geq 31$
- $2x_1 + 17x_3 + 4x_5 \geq 31$
- $2x_1 + 11x_2 + 7x_4 \geq 31$
- $8x_2 - 3x_4 \geq 0$
- $10x_3 - 9x_4 \geq 0$
- $13x_3 + 2x_4 \leq 65$
- $13x_3 + 11x_5 \leq 89$
- $17x_2 + 13x_3 \leq 41$
- $17x_2 + 2x_4 \leq 35$
- $14x_1 + 17x_2 \leq 97$
- $17x_2 + 11x_5 \leq 32$
- $2x_1 + 11x_2 + 17x_3 \leq 51$

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="roses", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="chili_plants", vtype=gurobi.GRB.INTEGER)
x3 = model.addVar(name="chrysanthemums", vtype=gurobi.GRB.INTEGER)
x4 = model.addVar(name="pansies", vtype=gurobi.GRB.INTEGER)
x5 = model.addVar(name="tomato_vines", vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(6.17 * x1 + 2.7 * x2 + 5.24 * x3 + 9.67 * x4 + 1.02 * x5, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(14 * x1 + 2 * x4 >= 22)
model.addConstr(17 * x2 + 2 * x4 >= 21)
model.addConstr(14 * x1 + 11 * x5 >= 26)
model.addConstr(14 * x1 + 17 * x2 >= 12)
model.addConstr(14 * x1 + 13 * x3 >= 13)
model.addConstr(14 * x1 + 17 * x2 + 13 * x3 + 2 * x4 + 11 * x5 >= 13)
model.addConstr(11 * x2 + 4 * x5 >= 41)
model.addConstr(2 * x1 + 7 * x4 >= 39)
model.addConstr(2 * x1 + 11 * x2 >= 23)
model.addConstr(11 * x2 + 17 * x3 >= 39)
model.addConstr(11 * x2 + 7 * x4 >= 49)
model.addConstr(2 * x1 + 4 * x5 >= 33)
model.addConstr(17 * x3 + 7 * x4 >= 20)
model.addConstr(7 * x4 + 4 * x5 >= 38)
model.addConstr(11 * x2 + 17 * x3 + 7 * x4 >= 38)
model.addConstr(11 * x2 + 17 * x3 + 4 * x5 >= 38)
model.addConstr(2 * x1 + 11 * x2 + 17 * x3 >= 38)
model.addConstr(17 * x3 + 7 * x4 + 4 * x5 >= 38)
model.addConstr(2 * x1 + 17 * x3 + 4 * x5 >= 38)
model.addConstr(2 * x1 + 17 * x3 + 7 * x4 >= 38)
model.addConstr(2 * x1 + 11 * x2 + 7 * x4 >= 38)
model.addConstr(11 * x2 + 17 * x3 + 4 * x5 >= 45)
model.addConstr(11 * x2 + 17 * x3 + 7 * x4 >= 45)
model.addConstr(2 * x1 + 11 * x2 + 17 * x3 >= 45)
model.addConstr(17 * x3 + 7 * x4 + 4 * x5 >= 45)
model.addConstr(2 * x1 + 17 * x3 + 4 * x5 >= 45)
model.addConstr(2 * x1 + 17 * x3 + 7 * x4 >= 45)
model.addConstr(2 * x1 + 11 * x2 + 7 * x4 >= 45)
model.addConstr(11 * x2 + 17 * x3 + 7 * x4 >= 41)
model.addConstr(11 * x2 + 17 * x3 + 4 * x5 >= 41)
model.addConstr(2 * x1 + 11 * x2 + 17 * x3 >= 41)
model.addConstr(17 * x3 + 7 * x4 + 4 * x5 >= 41)
model.addConstr(2 * x1 + 17 * x3 + 4 * x5 >= 41)
model.addConstr(2 * x1 + 17 * x3 + 7 * x4 >= 41)
model.addConstr(2 * x1 + 11 * x2 + 7 * x4 >= 41)
model.addConstr(8 * x2 - 3 * x4 >= 0)
model.addConstr(10 * x3 - 9 * x4 >= 0)
model.addConstr(13 * x3 + 2 * x4 <= 65)
model.addConstr(13 * x3 + 11 * x5 <= 89)
model.addConstr(17 * x2 + 13 * x3 <= 41)
model.addConstr(17 * x2 + 2 * x4 <= 35)
model.addConstr(14 * x1 + 17 * x2 <= 97)
model.addConstr(17 * x2 + 11 * x5 <= 32)
model.addConstr(2 * x1 + 11 * x2 + 17 * x3 <= 51)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("Roses: ", x1.varValue)
    print("Chili Plants: ", x2.varValue)
    print("Chrysanthemums: ", x3.varValue)
    print("Pansies: ", x4.varValue)
    print("Tomato Vines: ", x5.varValue)
else:
    print("The model is infeasible")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'roses'), 
        ('x2', 'chili plants'), 
        ('x3', 'chrysanthemums'), 
        ('x4', 'pansies'), 
        ('x5', 'tomato vines')
    ], 
    'objective_function': '6.17x1 + 2.7x2 + 5.24x3 + 9.67x4 + 1.02x5', 
    'constraints': [
        '14x1 + 2x4 >= 22',
        '17x2 + 2x4 >= 21',
        '14x1 + 11x5 >= 26',
        '14x1 + 17x2 >= 12',
        '14x1 + 13x3 >= 13',
        '14x1 + 17x2 + 13x3 + 2x4 + 11x5 >= 13',
        '11x2 + 4x5 >= 41',
        '2x1 + 7x4 >= 39',
        '2x1 + 11x2 >= 23',
        '11x2 + 17x3 >= 39',
        '11x2 + 7x4 >= 49',
        '2x1 + 4x5 >= 33',
        '17x3 + 7x4 >= 20',
        '7x4 + 4x5 >= 38',
        '11x2 + 17x3 + 7x4 >= 38',
        '11x2 + 17x3 + 4x5 >= 38',
        '2x1 + 11x2 + 17x3 >= 38',
        '17x3 + 7x4 + 4x5 >= 38',
        '2x1 + 17x3 + 4x5 >= 38',
        '2x1 + 17x3 + 7x4 >= 38',
        '2x1 + 11x2 + 7x4 >= 38',
        '8x2 - 3x4 >= 0',
        '10x3 - 9x4 >= 0',
        '13x3 + 2x4 <= 65',
        '13x3 + 11x5 <= 89',
        '17x2 + 13x3 <= 41',
        '17x2 + 2x4 <= 35',
        '14x1 + 17x2 <= 97',
        '17x2 + 11x5 <= 32',
        '2x1 + 11x2 + 17x3 <= 51'
    ]
}
```