## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'tomato vines', 'orange trees', 'chrysanthemums', and 'apple trees', which we can denote as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $8x_0 + 2x_1 + 7x_2 + 7x_3$.

## 3: List the constraints in symbolic notation
1. $10x_1 + 9x_2 + 4x_3 \geq 14$ (total combined growth speed from orange trees and chrysanthemums)
2. $3x_1 + 4x_2 + 8x_3 \geq 24$ (total planting space occupied by orange trees, chrysanthemums, and apple trees)
3. $8x_0 + 4x_2 + 8x_3 \geq 24$ (total planting space occupied by tomato vines, chrysanthemums, and apple trees)
4. $8x_0 + 3x_1 + 8x_3 \geq 24$ (total planting space occupied by tomato vines, orange trees, and apple trees)
5. $3x_1 + 4x_2 + 8x_3 \geq 30$ (orange trees, chrysanthemums, and apple trees must occupy at least 30 sq. ft)
6. $8x_0 + 4x_2 + 8x_3 \geq 30$ (tomato vines, chrysanthemums, and apple trees must occupy at least 30 ft^2)
7. $8x_0 + 3x_1 + 8x_3 \geq 30$ (total planting space occupied by tomato vines, orange trees, and apple trees must be 30 sq. ft or more)
8. $3x_1 + 4x_2 + 8x_3 \geq 33$ (orange trees, chrysanthemums, and apple trees must occupy at least 33 square feet)
9. $8x_0 + 4x_2 + 8x_3 \geq 33$ (tomato vines, chrysanthemums, and apple trees must occupy at least 33 square feet)
10. $8x_0 + 3x_1 + 8x_3 \geq 33$ (tomato vines, orange trees, and apple trees must take up at least 33 sq. ft)
11. $8x_0 + 9x_2 \leq 49$ (total combined growth speed from tomato vines and chrysanthemums)
12. $9x_2 + 4x_3 \leq 48$ (total combined growth speed from chrysanthemums and apple trees)
13. $10x_1 + 4x_3 \leq 20$ (total combined growth speed from orange trees and apple trees)
14. $8x_0 + 10x_1 \leq 66$ (total combined growth speed from tomato vines and orange trees)
15. $8x_0 + 4x_3 \leq 55$ (total combined growth speed from tomato vines and apple trees)
16. $10x_1 + 9x_2 + 4x_3 \leq 45$ (total combined growth speed from orange trees, chrysanthemums, and apple trees)
17. $8x_0 + 10x_1 + 4x_3 \leq 27$ (total combined growth speed from tomato vines, orange trees, and apple trees)
18. $8x_0 + 10x_1 + 9x_2 + 4x_3 \leq 27$ (total combined growth speed from all)
19. $3x_1 + 4x_2 \leq 111$ (orange trees and chrysanthemums must occupy at most 111 sq. ft)
20. $4x_2 + 8x_3 \leq 49$ (total planting space occupied by chrysanthemums and apple trees)
21. $8x_0 + 3x_1 \leq 64$ (total planting space occupied by tomato vines and orange trees)
22. $3x_1 + 8x_3 \leq 51$ (total planting space occupied by orange trees and apple trees)
23. $8x_0 + 4x_2 \leq 137$ (total planting space occupied by tomato vines and chrysanthemums)
24. $8x_0 + 3x_1 + 4x_2 \leq 36$ (total planting space occupied by tomato vines, orange trees, and chrysanthemums)
25. $8x_0 + 4x_2 + 8x_3 \leq 63$ (tomato vines, chrysanthemums, and apple trees must occupy at most 63 ft^2)
26. $8x_0 + 3x_1 + 4x_2 + 8x_3 \leq 63$ (total planting space occupied by all)

## 4: Define the symbolic variables
The symbolic variables are:
- $x_0$: tomato vines
- $x_1$: orange trees
- $x_2$: chrysanthemums
- $x_3$: apple trees

## 5: Write the Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="tomato_vines", vtype=gurobi.GRB.INTEGER)
x1 = model.addVar(name="orange_trees", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="chrysanthemums", vtype=gurobi.GRB.INTEGER)
x3 = model.addVar(name="apple_trees", vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(8*x0 + 2*x1 + 7*x2 + 7*x3, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(10*x1 + 9*x2 + 4*x3 >= 14)
model.addConstr(3*x1 + 4*x2 + 8*x3 >= 24)
model.addConstr(8*x0 + 4*x2 + 8*x3 >= 24)
model.addConstr(8*x0 + 3*x1 + 8*x3 >= 24)
model.addConstr(3*x1 + 4*x2 + 8*x3 >= 30)
model.addConstr(8*x0 + 4*x2 + 8*x3 >= 30)
model.addConstr(8*x0 + 3*x1 + 8*x3 >= 30)
model.addConstr(3*x1 + 4*x2 + 8*x3 >= 33)
model.addConstr(8*x0 + 4*x2 + 8*x3 >= 33)
model.addConstr(8*x0 + 3*x1 + 8*x3 >= 33)
model.addConstr(8*x0 + 9*x2 <= 49)
model.addConstr(9*x2 + 4*x3 <= 48)
model.addConstr(10*x1 + 4*x3 <= 20)
model.addConstr(8*x0 + 10*x1 <= 66)
model.addConstr(8*x0 + 4*x3 <= 55)
model.addConstr(10*x1 + 9*x2 + 4*x3 <= 45)
model.addConstr(8*x0 + 10*x1 + 4*x3 <= 27)
model.addConstr(8*x0 + 10*x1 + 9*x2 + 4*x3 <= 27)
model.addConstr(3*x1 + 4*x2 <= 111)
model.addConstr(4*x2 + 8*x3 <= 49)
model.addConstr(8*x0 + 3*x1 <= 64)
model.addConstr(3*x1 + 8*x3 <= 51)
model.addConstr(8*x0 + 4*x2 <= 137)
model.addConstr(8*x0 + 3*x1 + 4*x2 <= 36)
model.addConstr(8*x0 + 4*x2 + 8*x3 <= 63)
model.addConstr(8*x0 + 3*x1 + 4*x2 + 8*x3 <= 63)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Tomato Vines: ", x0.varValue)
    print("Orange Trees: ", x1.varValue)
    print("Chrysanthemums: ", x2.varValue)
    print("Apple Trees: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 6: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'tomato vines'),
        ('x1', 'orange trees'),
        ('x2', 'chrysanthemums'),
        ('x3', 'apple trees')
    ],
    'objective_function': '8*x0 + 2*x1 + 7*x2 + 7*x3',
    'constraints': [
        '10*x1 + 9*x2 + 4*x3 >= 14',
        '3*x1 + 4*x2 + 8*x3 >= 24',
        '8*x0 + 4*x2 + 8*x3 >= 24',
        '8*x0 + 3*x1 + 8*x3 >= 24',
        '3*x1 + 4*x2 + 8*x3 >= 30',
        '8*x0 + 4*x2 + 8*x3 >= 30',
        '8*x0 + 3*x1 + 8*x3 >= 30',
        '3*x1 + 4*x2 + 8*x3 >= 33',
        '8*x0 + 4*x2 + 8*x3 >= 33',
        '8*x0 + 3*x1 + 8*x3 >= 33',
        '8*x0 + 9*x2 <= 49',
        '9*x2 + 4*x3 <= 48',
        '10*x1 + 4*x3 <= 20',
        '8*x0 + 10*x1 <= 66',
        '8*x0 + 4*x3 <= 55',
        '10*x1 + 9*x2 + 4*x3 <= 45',
        '8*x0 + 10*x1 + 4*x3 <= 27',
        '8*x0 + 10*x1 + 9*x2 + 4*x3 <= 27',
        '3*x1 + 4*x2 <= 111',
        '4*x2 + 8*x3 <= 49',
        '8*x0 + 3*x1 <= 64',
        '3*x1 + 8*x3 <= 51',
        '8*x0 + 4*x2 <= 137',
        '8*x0 + 3*x1 + 4*x2 <= 36',
        '8*x0 + 4*x2 + 8*x3 <= 63',
        '8*x0 + 3*x1 + 4*x2 + 8*x3 <= 63'
    ]
}
```