## Symbolic Representation

To solve the given linear programming problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables:
- $x_1$ represents the number of bouquets of sunflowers sold.
- $x_2$ represents the number of bouquets of roses sold.

The objective is to maximize profit. The profit per bouquet of sunflowers sold is $7, and the profit per bouquet of roses sold is $12. Therefore, the objective function can be represented as:

Maximize: $7x_1 + 12x_2$

The constraints are as follows:
- Each bouquet of sunflowers needs 4 minutes of clipping, and each bouquet of roses requires 5 minutes of clipping. There are 1200 minutes available for clipping.
  - $4x_1 + 5x_2 \leq 1200$
- Each bouquet of sunflowers needs 3 minutes of packaging, and each bouquet of roses requires 7 minutes of packaging. There are 800 minutes available for packaging.
  - $3x_1 + 7x_2 \leq 800$
- At least 30 bouquets of sunflowers must be sold.
  - $x_1 \geq 30$
- There is no limit on the number of bouquets of roses sold.
  - $x_2 \geq 0$ (Implicitly, as there's no lower bound mentioned)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'bouquets of sunflowers'), ('x2', 'bouquets of roses')],
    'objective_function': '7*x1 + 12*x2',
    'constraints': [
        '4*x1 + 5*x2 <= 1200',
        '3*x1 + 7*x2 <= 800',
        'x1 >= 30',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_florist_problem():
    # Create a new model
    model = gp.Model("Tom's Florist")

    # Define variables
    x1 = model.addVar(name="sunflowers", lb=30, vtype=gp.GRB.CONTINUOUS)  # At least 30 bouquets of sunflowers
    x2 = model.addVar(name="roses", vtype=gp.GRB.CONTINUOUS)  # No limit on bouquets of roses

    # Objective function: Maximize profit
    model.setObjective(7 * x1 + 12 * x2, gp.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(4 * x1 + 5 * x2 <= 1200, name="clipping_time")
    model.addConstr(3 * x1 + 7 * x2 <= 800, name="packaging_time")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal solution found. Profit: ${model.objVal:.2f}")
        print(f"Bouquets of sunflowers: {x1.varValue:.2f}")
        print(f"Bouquets of roses: {x2.varValue:.2f}")
    else:
        print("No optimal solution found.")

solve_florist_problem()
```