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

- $x_1$ as the number of days the local farm operates,
- $x_2$ as the number of days the foreign farm operates.

The objective is to minimize the total cost while meeting the contract requirements for raspberries, bilberries, and strawberries.

Given:
- The cost per day at the local farm is $200, and at the foreign farm is $500.
- The harvest and delivery rates are 2.5 kg of raspberries, 3 kg of bilberries, and 2 kg of strawberries per day from the local farm, and 5 kg of raspberries, 4 kg of bilberries, and 4 kg of strawberries per day from the foreign farm.
- The contract requires 12 kg of raspberries, 10 kg of bilberries, and 20 kg of strawberries.

The symbolic representation can be summarized as:

```json
{
'sym_variables': [('x1', 'number of days local farm operates'), ('x2', 'number of days foreign farm operates')],
'objective_function': '200*x1 + 500*x2',
'constraints': [
'2.5*x1 + 5*x2 >= 12',  # Raspberries constraint
'3*x1 + 4*x2 >= 10',   # Bilberries constraint
'2*x1 + 4*x2 >= 20'    # Strawberries constraint
]
}
```

This representation captures the essence of the problem: minimizing the cost function `200*x1 + 500*x2` subject to meeting the demand for each type of berry.

To implement this in Gurobi using Python, we'll write the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="local_farm_days", vtype=GRB.CONTINUOUS)
x2 = m.addVar(name="foreign_farm_days", vtype=GRB.CONTINUOUS)

# Set the objective function
m.setObjective(200*x1 + 500*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(2.5*x1 + 5*x2 >= 12, name="raspberries_constraint")
m.addConstr(3*x1 + 4*x2 >= 10, name="bilberries_constraint")
m.addConstr(2*x1 + 4*x2 >= 20, name="strawberries_constraint")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Local farm operates for {x1.x} days")
    print(f"Foreign farm operates for {x2.x} days")
    print(f"Total cost: ${m.objVal}")
else:
    print("No optimal solution found.")

```