## Symbolic Representation

To solve Steven's investment problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, as well as the constraints.

### Variables
- $x_1$ : Investment in Delta
- $x_2$ : Investment in Omega

### Objective Function
The objective is to maximize the total profit, which is $0.8x_1 + 1.2x_2$.

### Constraints
1. Total budget constraint: $x_1 + x_2 \leq 100000$
2. Minimum investment in Delta: $x_1 \geq 0.25(x_1 + x_2)$
3. Minimum investment in Omega: $x_2 \geq 10000$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'Investment in Delta'), ('x2', 'Investment in Omega')],
    'objective_function': '0.8*x1 + 1.2*x2',
    'constraints': [
        'x1 + x2 <= 100000',
        'x1 >= 0.25*(x1 + x2)',
        'x2 >= 10000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_investment_problem():
    # Create a new model
    model = gp.Model("investment_problem")

    # Define variables
    x1 = model.addVar(name="Delta_Investment", lb=0)
    x2 = model.addVar(name="Omega_Investment", lb=0)

    # Objective function: Maximize 0.8*x1 + 1.2*x2
    model.setObjective(0.8*x1 + 1.2*x2, gp.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 100000, name="Total_Budget")
    model.addConstr(x1 >= 0.25*(x1 + x2), name="Min_Delta_Investment")
    model.addConstr(x2 >= 10000, name="Min_Omega_Investment")

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal Investment in Delta: ${x1.varValue:.2f}")
        print(f"Optimal Investment in Omega: ${x2.varValue:.2f}")
        print(f"Max Profit: ${model.objVal:.2f}")
    else:
        print("The model is infeasible.")

solve_investment_problem()
```