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

- $x_1$ as the number of winter jackets made daily,
- $x_2$ as the number of rain jackets made daily.

The objective function aims to maximize profit. Given that each winter jacket results in a $5 loss and each rain jacket results in a $50 profit, the objective function can be written as:

Maximize: $-5x_1 + 50x_2$

The constraints based on the problem description are:

1. At most 60 winter jackets can be made daily: $x_1 \leq 60$
2. At most 70 rain jackets can be made daily: $x_2 \leq 70$
3. A demand of at least 30 winter jackets must be met daily: $x_1 \geq 30$
4. A demand of at least 35 rain jackets must be met daily: $x_2 \geq 35$
5. A total of at least 80 jackets must be made daily to satisfy a contract: $x_1 + x_2 \geq 80$

Thus, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of winter jackets made daily'), ('x2', 'number of rain jackets made daily')],
    'objective_function': '-5*x1 + 50*x2',
    'constraints': ['x1 <= 60', 'x2 <= 70', 'x1 >= 30', 'x2 >= 35', 'x1 + x2 >= 80']
}
```

To solve this problem using Gurobi in Python, we'll use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=30, ub=60, vtype=GRB.INTEGER, name="winter_jackets")
x2 = m.addVar(lb=35, ub=70, vtype=GRB.INTEGER, name="rain_jackets")

# Set the objective function
m.setObjective(-5*x1 + 50*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 60, "max_winter_jackets")
m.addConstr(x2 <= 70, "max_rain_jackets")
m.addConstr(x1 >= 30, "min_winter_jackets")
m.addConstr(x2 >= 35, "min_rain_jackets")
m.addConstr(x1 + x2 >= 80, "total_jackets")

# Optimize the model
m.optimize()

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