To solve William's problem, we need to formulate a linear programming (LP) model that maximizes the number of potato packages transported under the given constraints.

Let's denote:
- $x_1$ as the number of regular truck trips,
- $x_2$ as the number of refrigerated truck trips.

The objective is to maximize the total number of potato packages transported, which can be represented by the objective function: $70x_1 + 100x_2$.

The constraints are:
1. The total cost must not exceed $5000: $50x_1 + 70x_2 \leq 5000$.
2. The number of refrigerated truck trips must not exceed the number of regular truck trips: $x_2 \leq x_1$.
3. Non-negativity constraints: $x_1 \geq 0$, $x_2 \geq 0$, since the number of trips cannot be negative.

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of regular truck trips'), ('x2', 'number of refrigerated truck trips')],
    'objective_function': '70*x1 + 100*x2',
    'constraints': ['50*x1 + 70*x2 <= 5000', 'x2 <= x1', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we can use the following code:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="regular_truck_trips", vtype=GRB.INTEGER, lb=0)
x2 = m.addVar(name="refrigerated_truck_trips", vtype=GRB.INTEGER, lb=0)

# Set the objective function
m.setObjective(70*x1 + 100*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(50*x1 + 70*x2 <= 5000, name="cost_constraint")
m.addConstr(x2 <= x1, name="trip_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Regular truck trips: {x1.x}")
    print(f"Refrigerated truck trips: {x2.x}")
    print(f"Total packages transported: {70*x1.x + 100*x2.x}")
else:
    print("No optimal solution found")
```