To solve Peter's optimization problem, let's first translate the natural language description into a symbolic representation.

Let:
- $x_1$ represent the amount of GreenCycle fertilizer used in kg.
- $x_2$ represent the amount of GrowSafe fertilizer used in kg.

The objective function is to minimize the total cost of the fertilizers. The cost of GreenCycle is $1.5 per kg, and the cost of GrowSafe is $1.8 per kg. Thus, the objective function can be written as:
\[ \text{Minimize:} \quad 1.5x_1 + 1.8x_2 \]

The constraints are based on the requirements for nitrous oxide and vitamin mix in the growth compound:
1. The compound must contain at least 9 units of nitrous oxide. Given that GreenCycle contains 2.1 units of nitrous oxide per kg and GrowSafe contains 3.5 units of nitrous oxide per kg, we have:
\[ 2.1x_1 + 3.5x_2 \geq 9 \]
2. The compound must contain at least 5 units of vitamin mix. Given that GreenCycle contains 1.3 units of vitamin mix per kg and GrowSafe contains 1.1 units of vitamin mix per kg, we have:
\[ 1.3x_1 + 1.1x_2 \geq 5 \]

Also, since Peter cannot use a negative amount of fertilizer, we have non-negativity constraints:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Thus, the symbolic representation of the problem in JSON format is:

```json
{
    'sym_variables': [('x1', 'GreenCycle fertilizer'), ('x2', 'GrowSafe fertilizer')],
    'objective_function': '1.5*x1 + 1.8*x2',
    'constraints': ['2.1*x1 + 3.5*x2 >= 9', '1.3*x1 + 1.1*x2 >= 5', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Peter'sCompound")

# Create variables
x1 = m.addVar(lb=0, name="GreenCycle")
x2 = m.addVar(lb=0, name="GrowSafe")

# Set the objective function
m.setObjective(1.5*x1 + 1.8*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(2.1*x1 + 3.5*x2 >= 9, "NitrousOxideConstraint")
m.addConstr(1.3*x1 + 1.1*x2 >= 5, "VitaminMixConstraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"GreenCycle: {x1.x}")
    print(f"GrowSafe: {x2.x}")
    print(f"Total Cost: {m.objVal}")
else:
    print("No optimal solution found")
```