To solve this problem, we first need to understand the constraints and the objective function. The goal is to maximize profit from selling regular pens (x1) and premium pens (x2), given their respective profits per unit ($3 for x1 and $8 for x2). There are constraints on daily demand: 0 ≤ x1 ≤ 100, 0 ≤ x2 ≤ 50, and a combined limit of x1 + x2 ≤ 75.

The objective function to maximize profit (P) is given by P = 3x1 + 8x2. The constraints can be summarized as follows:
1. 0 ≤ x1 ≤ 100
2. 0 ≤ x2 ≤ 50
3. x1 + x2 ≤ 75

We will use Gurobi, a powerful optimization library in Python, to solve this linear programming problem.

```python
from gurobipy import *

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

# Add variables: x1 for regular pens and x2 for premium pens
x1 = m.addVar(lb=0, ub=100, vtype=GRB.CONTINUOUS, name="Regular_Pens")
x2 = m.addVar(lb=0, ub=50, vtype=GRB.CONTINUOUS, name="Premium_Pens")

# Objective function: Maximize profit
m.setObjective(3*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 75, "Total_Pens_Constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: Sell {x1.x} regular pens and {x2.x} premium pens.")
else:
    print("No optimal solution found.")

```