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

- $x_1$ as the number of bottles of strawberry jam produced.
- $x_2$ as the number of bottles of peach jam produced.

The objective function 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:

\[ \text{Maximize:} \quad 3x_1 + 5x_2 \]

The constraints 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 total operational time of 3500 minutes per week.
\[ 20x_1 + 30x_2 \leq 3500 \]
2. Fruit availability for strawberry jam: At most 100 bottles can be made.
\[ x_1 \leq 100 \]
3. Fruit availability for peach jam: At most 80 bottles can be made.
\[ x_2 \leq 80 \]
4. Non-negativity constraints, as the number of bottles cannot be negative:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Symbolic representation in JSON format:

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

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="strawberry_jam")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="peach_jam")

# Set the objective function
m.setObjective(3*x1 + 5*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 30*x2 <= 3500, "time_constraint")
m.addConstr(x1 <= 100, "strawberry_availability")
m.addConstr(x2 <= 80, "peach_availability")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Strawberry jam bottles: {x1.x}")
    print(f"Peach jam bottles: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```