To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of black shoes made daily
- $x_2$ as the number of blue shoes made daily

The objective function aims to maximize net profits. Given that each black shoe sold results in a $3 loss and each blue shoe sold results in a $6 profit, the objective function can be represented algebraically as:

$$\text{Maximize: } -3x_1 + 6x_2$$

The constraints based on the problem description are:

1. The company can make at most 150 black shoes daily: $x_1 \leq 150$
2. The company can make at most 100 blue shoes daily: $x_2 \leq 100$
3. The expected demand for black shoes is at least 75 daily: $x_1 \geq 75$
4. The expected demand for blue shoes is at least 60 daily: $x_2 \geq 60$
5. A minimum of 125 shoes must be shipped each day: $x_1 + x_2 \geq 125$

Symbolic representation:
```json
{
  'sym_variables': [('x1', 'number of black shoes made daily'), ('x2', 'number of blue shoes made daily')],
  'objective_function': '-3*x1 + 6*x2',
  'constraints': ['x1 <= 150', 'x2 <= 100', 'x1 >= 75', 'x2 >= 60', 'x1 + x2 >= 125']
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=75, ub=150, vtype=GRB.INTEGER, name="black_shoes")
x2 = m.addVar(lb=60, ub=100, vtype=GRB.INTEGER, name="blue_shoes")

# Set the objective function
m.setObjective(-3*x1 + 6*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 150, "max_black_shoes")
m.addConstr(x2 <= 100, "max_blue_shoes")
m.addConstr(x1 >= 75, "min_black_shoes_demand")
m.addConstr(x2 >= 60, "min_blue_shoes_demand")
m.addConstr(x1 + x2 >= 125, "total_min_shoes")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Black shoes: {x1.x}")
    print(f"Blue shoes: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```