## Step 1: Define the symbolic representation of the variables
The variables are 'squash plants', 'chives', and 'orange trees', which we will denote as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $7x_1^2 + 9x_1x_2 + 2x_3^2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $23x_1 + 16x_2 \geq 129$
2. $23^2x_1^2 + 13^2x_3^2 \geq 84$
3. $23x_1 + 16x_2 + 13x_3 \geq 84$
4. $9x_2 - 3x_3 \geq 0$
5. $5x_1 - 7x_3 \geq 0$
6. $23x_1 + 16x_2 \leq 314$
7. $x_1$ is an integer (nonfractional)
8. $x_2$ is an integer
9. $x_3$ is an integer

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'squash plants'), ('x2', 'chives'), ('x3', 'orange trees')],
'objective_function': '7*x1^2 + 9*x1*x2 + 2*x3^2',
'constraints': [
    '23*x1 + 16*x2 >= 129',
    '23^2*x1^2 + 13^2*x3^2 >= 84',
    '23*x1 + 16*x2 + 13*x3 >= 84',
    '9*x2 - 3*x3 >= 0',
    '5*x1 - 7*x3 >= 0',
    '23*x1 + 16*x2 <= 314',
    'x1 is an integer',
    'x2 is an integer',
    'x3 is an integer'
]
}
```

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

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name='squash_plants', vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name='chives', vtype=gurobi.GRB.INTEGER)
x3 = model.addVar(name='orange_trees', vtype=gurobi.GRB.INTEGER)

# Set the objective function
model.setObjective(7*x1**2 + 9*x1*x2 + 2*x3**2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(23*x1 + 16*x2 >= 129)
model.addConstr(23**2*x1**2 + 13**2*x3**2 >= 84)
model.addConstr(23*x1 + 16*x2 + 13*x3 >= 84)
model.addConstr(9*x2 - 3*x3 >= 0)
model.addConstr(5*x1 - 7*x3 >= 0)
model.addConstr(23*x1 + 16*x2 <= 314)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', model.objval)
    print('squash plants: ', x1.varValue)
    print('chives: ', x2.varValue)
    print('orange trees: ', x3.varValue)
else:
    print('The model is infeasible')
```