## Problem Description and Symbolic Representation

The problem is a classic linear programming problem. We need to maximize the profit by determining the number of pants and shorts to produce, given the constraints on the availability of the measuring, cutting, and sewing teams.

Let's define the symbolic variables:
- $x_1$: number of pants
- $x_2$: number of shorts

The objective function is to maximize the profit:
- Maximize $5x_1 + 7x_2$

The constraints are:
- Measuring team: $0.5x_1 + 0.1x_2 \leq 60$
- Cutting team: $0.2x_1 + 0.5x_2 \leq 80$
- Sewing team: $0.7x_1 + 0.6x_2 \leq 75$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'pants'), ('x2', 'shorts')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '0.5*x1 + 0.1*x2 <= 60',
        '0.2*x1 + 0.5*x2 <= 80',
        '0.7*x1 + 0.6*x2 <= 75',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

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

# Define the objective function
model.setObjective(5*x1 + 7*x2, gp.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(0.5*x1 + 0.1*x2 <= 60, name="measuring")
model.addConstr(0.2*x1 + 0.5*x2 <= 80, name="cutting")
model.addConstr(0.7*x1 + 0.6*x2 <= 75, name="sewing")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Pants: {x1.varValue}")
    print(f"Shorts: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("No optimal solution found")
```