## Problem Description and Formulation

The problem is a linear programming (LP) optimization problem. Steven wants to invest in two pharmaceutical companies, Delta and Omega, with a total budget of at most $100,000. The profit per dollar invested in Delta is $0.80, and in Omega, it is $1.20. There are two constraints: 

1. A minimum of 25% of all money invested must be in Delta.
2. At least $10,000 must be invested in Omega.

The goal is to maximize the total profit earned from Steven's investment.

## Mathematical Formulation

Let's denote:
- \(x_D\) as the amount invested in Delta,
- \(x_O\) as the amount invested in Omega.

The objective function to maximize the total profit (\(P\)) is:
\[ P = 0.80x_D + 1.20x_O \]

Subject to:
1. Budget constraint: \( x_D + x_O \leq 100,000 \)
2. Delta investment constraint: \( x_D \geq 0.25(x_D + x_O) \)
3. Omega investment constraint: \( x_O \geq 10,000 \)
4. Non-negativity constraints: \( x_D \geq 0, x_O \geq 0 \)

## Simplifying Constraints

The Delta investment constraint can be simplified:
\[ x_D \geq 0.25x_D + 0.25x_O \]
\[ 0.75x_D \geq 0.25x_O \]
\[ 3x_D \geq x_O \]

## Gurobi Code

```python
import gurobi

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

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

    # Objective function: Maximize profit
    model.setObjective(0.80 * x_D + 1.20 * x_O, gurobi.GRB.MAXIMIZE)

    # Budget constraint
    model.addConstr(x_D + x_O <= 100000, name="Budget_Constraint")

    # Minimum Delta investment constraint
    model.addConstr(3 * x_D >= x_O, name="Delta_Min_Constraint")

    # Minimum Omega investment constraint
    model.addConstr(x_O >= 10000, name="Omega_Min_Constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Delta Investment: ${x_D.x:.2f}")
        print(f"Omega Investment: ${x_O.x:.2f}")
        print(f"Total Profit: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_investment_problem()
```