## Problem Description and Formulation

The problem is a linear programming optimization problem. Peter needs to produce a plant growth compound by mixing two types of fertilizer: GreenCycle and GrowSafe. The compound must contain at least 9 units of nitrous oxide and 5 units of vitamin mix. The goal is to minimize the cost of the compound.

Let's define the decision variables:

- $x_1$: the amount of GreenCycle fertilizer in kg
- $x_2$: the amount of GrowSafe fertilizer in kg

The objective function to minimize is the total cost:

- $1.5x_1 + 1.8x_2$

The constraints are:

- $2.1x_1 + 3.5x_2 \geq 9$ (at least 9 units of nitrous oxide)
- $1.3x_1 + 1.1x_2 \geq 5$ (at least 5 units of vitamin mix)
- $x_1 \geq 0, x_2 \geq 0$ (non-negativity constraints, as the amounts of fertilizers cannot be negative)

## Gurobi Code

```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the decision variables
    x1 = model.addVar(lb=0, name="GreenCycle")
    x2 = model.addVar(lb=0, name="GrowSafe")

    # Define the objective function
    model.setObjective(1.5 * x1 + 1.8 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(2.1 * x1 + 3.5 * x2 >= 9, name="Nitrous_Oxide")
    model.addConstr(1.3 * x1 + 1.1 * x2 >= 5, name="Vitamin_Mix")

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Minimum cost: ", model.objval)
        print("GreenCycle: ", x1.x)
        print("GrowSafe: ", x2.x)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```