## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables as follows:
- $x_1$ represents the number of bottles of strawberry jam.
- $x_2$ represents the number of bottles of peach jam.

The objective is to maximize profit. Given that the profit per bottle of strawberry jam is $3 and the profit per bottle of peach jam is $5, the objective function can be written as:

Maximize: $3x_1 + 5x_2$

The constraints based on the given information are:
1. Time constraint: It takes 20 minutes to make one bottle of strawberry jam and 30 minutes to make one bottle of peach jam, with a maximum of 3500 minutes per week.
   - $20x_1 + 30x_2 \leq 3500$

2. Strawberry jam production limit: They can make at most 100 bottles of strawberry jam.
   - $x_1 \leq 100$

3. Peach jam production limit: They can make at most 80 bottles of peach jam.
   - $x_2 \leq 80$

4. Non-negativity constraint: The number of bottles cannot be negative.
   - $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'bottles of strawberry jam'), ('x2', 'bottles of peach jam')],
    'objective_function': '3*x1 + 5*x2',
    'constraints': [
        '20*x1 + 30*x2 <= 3500',
        'x1 <= 100',
        'x2 <= 80',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = m.addVar(name="strawberry_jam", lb=0, ub=100, vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="peach_jam", lb=0, ub=80, vtype=gp.GRB.INTEGER)

# Objective function: Maximize 3*x1 + 5*x2
m.setObjective(3*x1 + 5*x2, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(20*x1 + 30*x2 <= 3500, name="time_constraint")
m.addConstr(x1 <= 100, name="strawberry_limit")
m.addConstr(x2 <= 80, name="peach_limit")

# Solve the model
m.optimize()

# Print the results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
    print(f"Maximum profit: ${3*x1.varValue + 5*x2.varValue}")
else:
    print("No optimal solution found.")
```