To solve this optimization problem, we first need to define the variables and the objective function symbolically. Let's denote:

- $x_1$ as the number of blue t-shirts made,
- $x_2$ as the number of dark blue t-shirts made.

The objective function aims to maximize profit. Given that a blue t-shirt yields a profit of $10 and a dark blue t-shirt yields a profit of $15, the objective function can be represented symbolically as:

\[ \text{Maximize:} \quad 10x_1 + 15x_2 \]

The constraints are based on the availability of resources:
- Dye: Each blue t-shirt requires 3 units, and each dark blue t-shirt requires 5 units. The company has 1000 units available.
- Water: Each blue t-shirt requires 5 units, and each dark blue t-shirt requires 4 units. The company has 1200 units available.
- Worker minutes: Each blue t-shirt requires 30 minutes, and each dark blue t-shirt requires 25 minutes. The company has 8000 minutes available.

Thus, the symbolic representation of the constraints is:
- Dye constraint: $3x_1 + 5x_2 \leq 1000$
- Water constraint: $5x_1 + 4x_2 \leq 1200$
- Worker minutes constraint: $30x_1 + 25x_2 \leq 8000$

Additionally, since the number of t-shirts cannot be negative:
- Non-negativity constraints: $x_1 \geq 0$, $x_2 \geq 0$

The symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'blue t-shirts'), ('x2', 'dark blue t-shirts')],
    'objective_function': '10*x1 + 15*x2',
    'constraints': [
        '3*x1 + 5*x2 <= 1000',
        '5*x1 + 4*x2 <= 1200',
        '30*x1 + 25*x2 <= 8000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

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

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="blue_tshirts")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="dark_blue_tshirts")

# Set the objective function
m.setObjective(10*x1 + 15*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 + 5*x2 <= 1000, "dye_constraint")
m.addConstr(5*x1 + 4*x2 <= 1200, "water_constraint")
m.addConstr(30*x1 + 25*x2 <= 8000, "worker_minutes_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Blue t-shirts: {x1.x}")
    print(f"Dark blue t-shirts: {x2.x}")
    print(f"Maximum profit: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```