To solve Frank's investment problem, we first need to translate the natural language description into a symbolic representation. Let's define:

- $x_1$ as the amount invested in the cigarette industry.
- $x_2$ as the amount invested in the tobacco industry.

The objective is to maximize the total profit from these investments. Given that each dollar invested in the cigarette industry yields a $0.30 profit and each dollar invested in the tobacco industry yields a $0.45 profit, the objective function can be represented as:

Maximize: $0.30x_1 + 0.45x_2$

The constraints are:
1. The total amount invested cannot exceed $5000: $x_1 + x_2 \leq 5000$
2. At least 40% of all the money invested must be in the cigarette industry: $x_1 \geq 0.4(x_1 + x_2)$
3. At least $1000 must be invested in the tobacco industry: $x_2 \geq 1000$
4. Non-negativity constraints, since investments cannot be negative: $x_1 \geq 0$, $x_2 \geq 0$

In symbolic representation with natural language objects:

```json
{
    'sym_variables': [('x1', 'amount invested in the cigarette industry'), ('x2', 'amount invested in the tobacco industry')],
    'objective_function': 'Maximize: 0.30*x1 + 0.45*x2',
    'constraints': ['x1 + x2 <= 5000', 'x1 >= 0.4*(x1 + x2)', 'x2 >= 1000', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

# Create a new model
m = Model("Frank_Investment")

# Define variables
x1 = m.addVar(lb=0, name="cigarette_investment")
x2 = m.addVar(lb=0, name="tobacco_investment")

# Set the objective function
m.setObjective(0.30*x1 + 0.45*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 5000, "total_investment")
m.addConstr(x1 >= 0.4*(x1 + x2), "cigarette_percentage")
m.addConstr(x2 >= 1000, "tobacco_minimum")

# Optimize the model
m.optimize()

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