## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize the profit from selling bouquets of daisies and lilies given certain constraints on clipping and packaging time, as well as a contractual obligation to pick a minimum number of bouquets of daisies.

Let's define the variables:
- \(x\): The number of bouquets of daisies.
- \(y\): The number of bouquets of lilies.

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 5x + 4y \]

The constraints are:
1. Clipping time: \(3x + y \leq 1000\)
2. Packaging time: \(2x + 3y \leq 650\)
3. Minimum bouquets of daisies: \(x \geq 25\)
4. Non-negativity: \(x \geq 0, y \geq 0\)

Since \(x\) and \(y\) represent the number of bouquets, they must be integers. However, for the purpose of this LP formulation, we'll first solve it as a linear program and then consider if integer constraints are necessary.

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x = model.addVar(lb=25, name="daisies")  # At least 25 bouquets of daisies
    y = model.addVar(lb=0, name="lilies")   # No limit on bouquets of lilies

    # Objective function: Maximize profit
    model.setObjective(5 * x + 4 * y, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(3 * x + y <= 1000, name="clipping_time")
    model.addConstr(2 * x + 3 * y <= 650, name="packaging_time")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal profit: ", model.objVal)
        print("Bouquets of daisies: ", x.varValue)
        print("Bouquets of lilies: ", y.varValue)
    else:
        print("The model is infeasible")

solve_garden_problem()
```

This code sets up the linear programming problem using Gurobi, solves it, and then prints out the optimal profit and the quantities of bouquets of daisies and lilies to achieve this profit. If the problem is infeasible (for example, if the constraints cannot be satisfied), it will indicate that instead. 

Note that this solution assumes that fractional bouquets can be sold. If only whole bouquets can be sold, the problem would need to be formulated as an integer program by adding `x.Integers = True` and `y.Integers = True` after defining `x` and `y`.