## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The family business wants to maximize their profit by producing the optimal number of bottles of strawberry jam and peach jam.

Let's define the decision variables:

* `x`: number of bottles of strawberry jam produced
* `y`: number of bottles of peach jam produced

The objective function is to maximize the total profit:

* Profit per bottle of strawberry jam: $3
* Profit per bottle of peach jam: $5
* Total profit: `3x + 5y`

The constraints are:

* Time constraint: The family business operates for 3500 minutes per week.
	+ Time to make one bottle of strawberry jam: 20 minutes
	+ Time to make one bottle of peach jam: 30 minutes
	+ Total time: `20x + 30y <= 3500`
* Fruit availability constraints:
	+ Maximum number of bottles of strawberry jam: 100
		- `x <= 100`
	+ Maximum number of bottles of peach jam: 80
		- `y <= 80`
* Non-negativity constraints:
	+ `x >= 0`
	+ `y >= 0`

## Gurobi Code

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the decision variables
x = model.addVar(lb=0, ub=100, name="strawberry_jam")
y = model.addVar(lb=0, ub=80, name="peach_jam")

# Set the objective function
model.setObjective(3*x + 5*y, gurobi.GRB.MAXIMIZE)

# Add the time constraint
model.addConstr(20*x + 30*y <= 3500, name="time_constraint")

# Add the fruit availability constraints
model.addConstr(x <= 100, name="strawberry_jam_constraint")
model.addConstr(y <= 80, name="peach_jam_constraint")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Number of bottles of strawberry jam: {x.varValue}")
    print(f"Number of bottles of peach jam: {y.varValue}")
    print(f"Maximum profit: {model.objVal}")
else:
    print("No optimal solution found.")
```