To solve Steven's investment problem, we first need to define the decision variables and the objective function. Let's denote the amount invested in Delta as \(D\) and the amount invested in Omega as \(O\). The objective is to maximize the total profit, which can be calculated as \(0.80D + 1.20O\).

Given constraints are:
1. Total budget constraint: \(D + O \leq 100000\)
2. Minimum investment in Delta: \(D \geq 0.25(D + O)\)
3. Minimum investment in Omega: \(O \geq 10000\)

We also need to ensure that both \(D\) and \(O\) are non-negative since negative investments do not make sense in this context.

Now, let's formulate the Linear Programming (LP) problem:

- **Decision Variables:**\(D, O\)
- **Objective Function:** Maximize \(0.80D + 1.20O\)
- **Constraints:**
  - \(D + O \leq 100000\)
  - \(D \geq 0.25(D + O)\) which simplifies to \(0.75D \geq 0.25O\) or \(3D \geq O\)
  - \(O \geq 10000\)
  - \(D, O \geq 0\)

Let's simplify the second constraint further for clarity in coding: 
\(3D \geq O\) can be represented directly as is.

Here is how we translate this into Gurobi code:

```python
from gurobipy import *

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

# Decision Variables
D = m.addVar(name='Delta', vtype=GRB.CONTINUOUS, lb=0)
O = m.addVar(name='Omega', vtype=GRB.CONTINUOUS, lb=0)

# Objective Function: Maximize profit
m.setObjective(0.80*D + 1.20*O, GRB.MAXIMIZE)

# Constraints
m.addConstr(D + O <= 100000, name='Budget_Constraint')
m.addConstr(3*D >= O, name='Delta_Minimum_Constraint')
m.addConstr(O >= 10000, name='Omega_Minimum_Constraint')

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print('Optimal solution found:')
    print('Invest in Delta: $', D.x)
    print('Invest in Omega: $', O.x)
    print('Total Profit: $', m.objVal)
else:
    print('No optimal solution found')
```