## Problem Description and Symbolic Representation

The problem is a linear programming optimization problem. The goal is to maximize profit by determining the number of grey and black pants to produce, given the processing time constraints at two factories, Wimo and Webo.

### Symbolic Representation

Let's define the symbolic variables:
- $x_1$: Number of grey pants
- $x_2$: Number of black pants

The objective function is to maximize profit. Given that the cost per pair of grey pants is $25 and the cost per pair of black pants is $15, the objective function can be represented as:

Maximize: $25x_1 + 15x_2$

The constraints are:
- Each pair of grey pants requires 40 minutes of processing time at Wimo, and each pair of black pants requires 20 minutes. Wimo is available for 2100 minutes.
- Each pair of grey pants requires 30 minutes of processing time at Webo, and each pair of black pants requires 15 minutes. Webo is available for 3000 minutes.
- The number of pants cannot be negative.

These constraints can be represented as:
- $40x_1 + 20x_2 \leq 2100$
- $30x_1 + 15x_2 \leq 3000$
- $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'grey pants'), ('x2', 'black pants')],
    'objective_function': '25*x1 + 15*x2',
    'constraints': [
        '40*x1 + 20*x2 <= 2100',
        '30*x1 + 15*x2 <= 3000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Pants_Production")

# Define the variables
x1 = model.addVar(name="grey_pants", lb=0, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="black_pants", lb=0, vtype=gp.GRB.CONTINUOUS)

# Define the objective function
model.setObjective(25*x1 + 15*x2, gp.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(40*x1 + 20*x2 <= 2100, name="Wimo_constraint")
model.addConstr(30*x1 + 15*x2 <= 3000, name="Webo_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Number of grey pants: {x1.varValue}")
    print(f"Number of black pants: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("The model is infeasible or unbounded.")
```