## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize the number of potato packages transported under certain constraints.

### Variables:
- Let \(R\) be the number of regular truck trips.
- Let \(r\) be the number of refrigerated truck trips.

### Objective Function:
The objective is to maximize the total number of potato packages transported. The number of packages transported by regular trucks is \(70R\) and by refrigerated trucks is \(100r\). Therefore, the objective function is:
\[ \text{Maximize:} \quad 70R + 100r \]

### Constraints:
1. **Cost Constraint:** The total cost must not exceed $5000. The cost for regular truck trips is $50\(R\) and for refrigerated truck trips is $70\(r\). Therefore:
\[ 50R + 70r \leq 5000 \]

2. **Refrigerated vs. Regular Trips Constraint:** The number of refrigerated truck trips must not exceed the number of regular truck trips:
\[ r \leq R \]

3. **Non-Negativity Constraint:** The number of trips cannot be negative:
\[ R \geq 0, \quad r \geq 0 \]

## Gurobi Code

```python
import gurobi

def solve_potato_transportation_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    R = model.addVar(lb=0, name="Regular_Truck_Trips", vtype=gurobi.GRB.CONTINUOUS)
    r = model.addVar(lb=0, name="Refrigerated_Truck_Trips", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Maximize 70R + 100r
    model.setObjective(70*R + 100*r, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(50*R + 70*r <= 5000, name="Cost_Constraint")
    model.addConstr(r <= R, name="Refrigerated_vs_Regular_Trips")

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Solution: Regular Truck Trips = {R.varValue}, Refrigerated Truck Trips = {r.varValue}")
        print(f"Maximum Packages Transported: {70*R.varValue + 100*r.varValue}")
    else:
        print("The model is infeasible or unbounded.")

solve_potato_transportation_problem()
```