To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of red and green shirts produced, formulating the objective function that represents the total profit, and listing the constraints based on the limited resources (dye, water, and worker minutes).

Let's define:
- \(x_1\) as the number of red shirts produced,
- \(x_2\) as the number of green shirts produced.

The objective function, which is to maximize profit, can be represented as:
\[20x_1 + 35x_2\]

Given that each red shirt requires 2 units of dye, 5 units of water, and 20 worker minutes, and each green shirt requires 5 units of dye, 8 units of water, and 25 worker minutes, the constraints can be formulated as follows:
1. Dye constraint: \(2x_1 + 5x_2 \leq 1500\)
2. Water constraint: \(5x_1 + 8x_2 \leq 3000\)
3. Worker minutes constraint: \(20x_1 + 25x_2 \leq 8000\)

Also, \(x_1 \geq 0\) and \(x_2 \geq 0\) since the number of shirts produced cannot be negative.

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of red shirts'), ('x2', 'number of green shirts')],
    'objective_function': '20*x1 + 35*x2',
    'constraints': [
        '2*x1 + 5*x2 <= 1500',
        '5*x1 + 8*x2 <= 3000',
        '20*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("Fancy_Clothing-Co")

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="red_shirts", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="green_shirts", lb=0)

# Set the objective function
m.setObjective(20*x1 + 35*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x1 + 5*x2 <= 1500, "dye_constraint")
m.addConstr(5*x1 + 8*x2 <= 3000, "water_constraint")
m.addConstr(20*x1 + 25*x2 <= 8000, "worker_minutes_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Red shirts: {x1.x}")
    print(f"Green shirts: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```