## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the acres of daisies
- $x_2$ represents the acres of peonies

## Step 2: Formulate the objective function
The profit per acre of daisies is $150, and the profit per acre of peonies is $180. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 150x_1 + 180x_2 \]

## 3: Define the constraints
1. Hudson has 55 acres in total: $x_1 + x_2 \leq 55$
2. Daisies require 4.5 kg of plant nutrition per acre, and peonies require 7 kg of plant nutrition per acre. Hudson wants to use at most 200 kg of plant nutrition: $4.5x_1 + 7x_2 \leq 200$
3. Acres cannot be negative: $x_1 \geq 0, x_2 \geq 0$

## 4: Symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'acres of daisies'), ('x2', 'acres of peonies')],
    'objective_function': '150*x1 + 180*x2',
    'constraints': [
        'x1 + x2 <= 55',
        '4.5*x1 + 7*x2 <= 200',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 5: Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="daisies")
    x2 = model.addVar(lb=0, name="peonies")

    # Objective function
    model.setObjective(150*x1 + 180*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 + x2 <= 55, name="total_acres")
    model.addConstr(4.5*x1 + 7*x2 <= 200, name="plant_nutrition")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Acres of daisies: {x1.varValue}")
        print(f"Acres of peonies: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```