## Problem Description and Symbolic Representation

The hiker wants to minimize the cost of purchasing berry mixes A and B while ensuring he eats at least 150g of blueberries and 125g of blackberries.

### Symbolic Variables:
- $x_1$ : Number of bags of berry mix A
- $x_2$ : Number of bags of berry mix B

### Objective Function:
The objective is to minimize the total cost. Berry mix A costs $5 per bag, and berry mix B costs $3 per bag. So, the objective function is:
\[ \text{Minimize:} \quad 5x_1 + 3x_2 \]

### Constraints:
1. Blueberries constraint: The hiker needs at least 150g of blueberries. Berry mix A contains 30g of blueberries per bag, and berry mix B contains 20g of blueberries per bag.
\[ 30x_1 + 20x_2 \geq 150 \]
2. Blackberries constraint: The hiker needs at least 125g of blackberries. Berry mix A contains 45g of blackberries per bag, and berry mix B contains 15g of blackberries per bag.
\[ 45x_1 + 15x_2 \geq 125 \]
3. Non-negativity constraint: The number of bags cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'bags of berry mix A'), ('x2', 'bags of berry mix B')],
    'objective_function': '5*x1 + 3*x2',
    'constraints': [
        '30*x1 + 20*x2 >= 150',
        '45*x1 + 15*x2 >= 125',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("berry_mix")

# Define variables
x1 = model.addVar(name="berry_mix_A", lb=0, vtype=gp.GRB.INTEGER)  # Number of bags of berry mix A
x2 = model.addVar(name="berry_mix_B", lb=0, vtype=gp.GRB.INTEGER)  # Number of bags of berry mix B

# Objective function: Minimize cost
model.setObjective(5 * x1 + 3 * x2, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(30 * x1 + 20 * x2 >= 150, name="blueberries_constraint")
model.addConstr(45 * x1 + 15 * x2 >= 125, name="blackberries_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
    print(f"Minimum cost: ${5 * x1.varValue + 3 * x2.varValue}")
else:
    print("No optimal solution found.")
```